4.Credit Risk Modeling_LGD & EAD Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Credit Risk Modeling: LGD & EAD Model\n",
    "*Author: Shawn Sun*\n",
    "<br>\n",
    "*Date: 2021/01/29*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Import Libraries and Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda3\\lib\\site-packages\\IPython\\core\\interactiveshell.py:3146: DtypeWarning: Columns (21,49) have mixed types.Specify dtype option on import or set low_memory=False.\n",
      "  has_raised = await self.run_ast_nodes(code_ast.body, cell_name,\n"
     ]
    }
   ],
   "source": [
    "loan_data_preprocessed_backup = pd.read_csv('loan_data_2007_2014_preprocessed.csv')\n",
    "loan_data_preprocessed = loan_data_preprocessed_backup.copy()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Explore Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['Unnamed: 0', 'Unnamed: 0.1', 'id', 'member_id', 'loan_amnt',\n",
       "       'funded_amnt', 'funded_amnt_inv', 'term', 'int_rate',\n",
       "       'installment', 'grade', 'sub_grade', 'emp_title', 'emp_length',\n",
       "       'home_ownership', 'annual_inc', 'verification_status', 'issue_d',\n",
       "       'loan_status', 'pymnt_plan', 'url', 'desc', 'purpose', 'title',\n",
       "       'zip_code', 'addr_state', 'dti', 'delinq_2yrs', 'earliest_cr_line',\n",
       "       'inq_last_6mths', 'mths_since_last_delinq',\n",
       "       'mths_since_last_record', 'open_acc', 'pub_rec', 'revol_bal',\n",
       "       'revol_util', 'total_acc', 'initial_list_status', 'out_prncp',\n",
       "       'out_prncp_inv', 'total_pymnt', 'total_pymnt_inv',\n",
       "       'total_rec_prncp', 'total_rec_int', 'total_rec_late_fee',\n",
       "       'recoveries', 'collection_recovery_fee', 'last_pymnt_d',\n",
       "       'last_pymnt_amnt', 'next_pymnt_d', 'last_credit_pull_d',\n",
       "       'collections_12_mths_ex_med', 'mths_since_last_major_derog',\n",
       "       'policy_code', 'application_type', 'annual_inc_joint', 'dti_joint',\n",
       "       'verification_status_joint', 'acc_now_delinq', 'tot_coll_amt',\n",
       "       'tot_cur_bal', 'open_acc_6m', 'open_il_6m', 'open_il_12m',\n",
       "       'open_il_24m', 'mths_since_rcnt_il', 'total_bal_il', 'il_util',\n",
       "       'open_rv_12m', 'open_rv_24m', 'max_bal_bc', 'all_util',\n",
       "       'total_rev_hi_lim', 'inq_fi', 'total_cu_tl', 'inq_last_12m',\n",
       "       'emp_length_int', 'earliest_cr_line_date',\n",
       "       'mths_since_earliest_cr_line', 'term_int', 'issue_d_date',\n",
       "       'mths_since_issue_d', 'grade:A', 'grade:B', 'grade:C', 'grade:D',\n",
       "       'grade:E', 'grade:F', 'grade:G', 'sub_grade:A1', 'sub_grade:A2',\n",
       "       'sub_grade:A3', 'sub_grade:A4', 'sub_grade:A5', 'sub_grade:B1',\n",
       "       'sub_grade:B2', 'sub_grade:B3', 'sub_grade:B4', 'sub_grade:B5',\n",
       "       'sub_grade:C1', 'sub_grade:C2', 'sub_grade:C3', 'sub_grade:C4',\n",
       "       'sub_grade:C5', 'sub_grade:D1', 'sub_grade:D2', 'sub_grade:D3',\n",
       "       'sub_grade:D4', 'sub_grade:D5', 'sub_grade:E1', 'sub_grade:E2',\n",
       "       'sub_grade:E3', 'sub_grade:E4', 'sub_grade:E5', 'sub_grade:F1',\n",
       "       'sub_grade:F2', 'sub_grade:F3', 'sub_grade:F4', 'sub_grade:F5',\n",
       "       'sub_grade:G1', 'sub_grade:G2', 'sub_grade:G3', 'sub_grade:G4',\n",
       "       'sub_grade:G5', 'home_ownership:ANY', 'home_ownership:MORTGAGE',\n",
       "       'home_ownership:NONE', 'home_ownership:OTHER',\n",
       "       'home_ownership:OWN', 'home_ownership:RENT',\n",
       "       'verification_status:Not Verified',\n",
       "       'verification_status:Source Verified',\n",
       "       'verification_status:Verified', 'loan_status:Charged Off',\n",
       "       'loan_status:Current', 'loan_status:Default',\n",
       "       'loan_status:Does not meet the credit policy. Status:Charged Off',\n",
       "       'loan_status:Does not meet the credit policy. Status:Fully Paid',\n",
       "       'loan_status:Fully Paid', 'loan_status:In Grace Period',\n",
       "       'loan_status:Late (16-30 days)', 'loan_status:Late (31-120 days)',\n",
       "       'purpose:car', 'purpose:credit_card', 'purpose:debt_consolidation',\n",
       "       'purpose:educational', 'purpose:home_improvement', 'purpose:house',\n",
       "       'purpose:major_purchase', 'purpose:medical', 'purpose:moving',\n",
       "       'purpose:other', 'purpose:renewable_energy',\n",
       "       'purpose:small_business', 'purpose:vacation', 'purpose:wedding',\n",
       "       'addr_state:AK', 'addr_state:AL', 'addr_state:AR', 'addr_state:AZ',\n",
       "       'addr_state:CA', 'addr_state:CO', 'addr_state:CT', 'addr_state:DC',\n",
       "       'addr_state:DE', 'addr_state:FL', 'addr_state:GA', 'addr_state:HI',\n",
       "       'addr_state:IA', 'addr_state:ID', 'addr_state:IL', 'addr_state:IN',\n",
       "       'addr_state:KS', 'addr_state:KY', 'addr_state:LA', 'addr_state:MA',\n",
       "       'addr_state:MD', 'addr_state:ME', 'addr_state:MI', 'addr_state:MN',\n",
       "       'addr_state:MO', 'addr_state:MS', 'addr_state:MT', 'addr_state:NC',\n",
       "       'addr_state:NE', 'addr_state:NH', 'addr_state:NJ', 'addr_state:NM',\n",
       "       'addr_state:NV', 'addr_state:NY', 'addr_state:OH', 'addr_state:OK',\n",
       "       'addr_state:OR', 'addr_state:PA', 'addr_state:RI', 'addr_state:SC',\n",
       "       'addr_state:SD', 'addr_state:TN', 'addr_state:TX', 'addr_state:UT',\n",
       "       'addr_state:VA', 'addr_state:VT', 'addr_state:WA', 'addr_state:WI',\n",
       "       'addr_state:WV', 'addr_state:WY', 'initial_list_status:f',\n",
       "       'initial_list_status:w', 'good_bad'], dtype=object)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_preprocessed.columns.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>id</th>\n",
       "      <th>member_id</th>\n",
       "      <th>loan_amnt</th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>funded_amnt_inv</th>\n",
       "      <th>term</th>\n",
       "      <th>int_rate</th>\n",
       "      <th>installment</th>\n",
       "      <th>...</th>\n",
       "      <th>addr_state:UT</th>\n",
       "      <th>addr_state:VA</th>\n",
       "      <th>addr_state:VT</th>\n",
       "      <th>addr_state:WA</th>\n",
       "      <th>addr_state:WI</th>\n",
       "      <th>addr_state:WV</th>\n",
       "      <th>addr_state:WY</th>\n",
       "      <th>initial_list_status:f</th>\n",
       "      <th>initial_list_status:w</th>\n",
       "      <th>good_bad</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1077501</td>\n",
       "      <td>1296599</td>\n",
       "      <td>5000</td>\n",
       "      <td>5000</td>\n",
       "      <td>4975.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>10.65</td>\n",
       "      <td>162.87</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1077430</td>\n",
       "      <td>1314167</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>15.27</td>\n",
       "      <td>59.83</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1077175</td>\n",
       "      <td>1313524</td>\n",
       "      <td>2400</td>\n",
       "      <td>2400</td>\n",
       "      <td>2400.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>15.96</td>\n",
       "      <td>84.33</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>1076863</td>\n",
       "      <td>1277178</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>13.49</td>\n",
       "      <td>339.31</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>1075358</td>\n",
       "      <td>1311748</td>\n",
       "      <td>3000</td>\n",
       "      <td>3000</td>\n",
       "      <td>3000.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>12.69</td>\n",
       "      <td>67.79</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 209 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Unnamed: 0.1       id  member_id  loan_amnt  funded_amnt  \\\n",
       "0           0             0  1077501    1296599       5000         5000   \n",
       "1           1             1  1077430    1314167       2500         2500   \n",
       "2           2             2  1077175    1313524       2400         2400   \n",
       "3           3             3  1076863    1277178      10000        10000   \n",
       "4           4             4  1075358    1311748       3000         3000   \n",
       "\n",
       "   funded_amnt_inv        term  int_rate  installment  ... addr_state:UT  \\\n",
       "0           4975.0   36 months     10.65       162.87  ...             0   \n",
       "1           2500.0   60 months     15.27        59.83  ...             0   \n",
       "2           2400.0   36 months     15.96        84.33  ...             0   \n",
       "3          10000.0   36 months     13.49       339.31  ...             0   \n",
       "4           3000.0   60 months     12.69        67.79  ...             0   \n",
       "\n",
       "  addr_state:VA addr_state:VT addr_state:WA addr_state:WI  addr_state:WV  \\\n",
       "0             0             0             0             0              0   \n",
       "1             0             0             0             0              0   \n",
       "2             0             0             0             0              0   \n",
       "3             0             0             0             0              0   \n",
       "4             0             0             0             0              0   \n",
       "\n",
       "  addr_state:WY initial_list_status:f initial_list_status:w good_bad  \n",
       "0             0                     1                     0        1  \n",
       "1             0                     1                     0        0  \n",
       "2             0                     1                     0        1  \n",
       "3             0                     1                     0        1  \n",
       "4             0                     1                     0        1  \n",
       "\n",
       "[5 rows x 209 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_preprocessed.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_data_defaults = \\\n",
    "loan_data_preprocessed\\\n",
    "[loan_data_preprocessed['loan_status'].isin(['Charged Off',\n",
    "                                             'Does not meet the credit policy. Status:Charged Off'])]\n",
    "# Take only the accounts that were charged-off (written-off) as defaulted accounts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(43236, 209)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_defaults.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "pd.options.display.max_rows = None"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unnamed: 0                                                             0\n",
       "Unnamed: 0.1                                                           0\n",
       "id                                                                     0\n",
       "member_id                                                              0\n",
       "loan_amnt                                                              0\n",
       "funded_amnt                                                            0\n",
       "funded_amnt_inv                                                        0\n",
       "term                                                                   0\n",
       "int_rate                                                               0\n",
       "installment                                                            0\n",
       "grade                                                                  0\n",
       "sub_grade                                                              0\n",
       "emp_title                                                           3287\n",
       "emp_length                                                          2337\n",
       "home_ownership                                                         0\n",
       "annual_inc                                                             0\n",
       "verification_status                                                    0\n",
       "issue_d                                                                0\n",
       "loan_status                                                            0\n",
       "pymnt_plan                                                             0\n",
       "url                                                                    0\n",
       "desc                                                               27396\n",
       "purpose                                                                0\n",
       "title                                                                  3\n",
       "zip_code                                                               0\n",
       "addr_state                                                             0\n",
       "dti                                                                    0\n",
       "delinq_2yrs                                                            0\n",
       "earliest_cr_line                                                       3\n",
       "inq_last_6mths                                                         0\n",
       "mths_since_last_delinq                                             23950\n",
       "mths_since_last_record                                             37821\n",
       "open_acc                                                               0\n",
       "pub_rec                                                                0\n",
       "revol_bal                                                              0\n",
       "revol_util                                                            53\n",
       "total_acc                                                              0\n",
       "initial_list_status                                                    0\n",
       "out_prncp                                                              0\n",
       "out_prncp_inv                                                          0\n",
       "total_pymnt                                                            0\n",
       "total_pymnt_inv                                                        0\n",
       "total_rec_prncp                                                        0\n",
       "total_rec_int                                                          0\n",
       "total_rec_late_fee                                                     0\n",
       "recoveries                                                             0\n",
       "collection_recovery_fee                                                0\n",
       "last_pymnt_d                                                         376\n",
       "last_pymnt_amnt                                                        0\n",
       "next_pymnt_d                                                       42475\n",
       "last_credit_pull_d                                                     6\n",
       "collections_12_mths_ex_med                                            28\n",
       "mths_since_last_major_derog                                        35283\n",
       "policy_code                                                            0\n",
       "application_type                                                       0\n",
       "annual_inc_joint                                                   43236\n",
       "dti_joint                                                          43236\n",
       "verification_status_joint                                          43236\n",
       "acc_now_delinq                                                         0\n",
       "tot_coll_amt                                                       10780\n",
       "tot_cur_bal                                                        10780\n",
       "open_acc_6m                                                        43236\n",
       "open_il_6m                                                         43236\n",
       "open_il_12m                                                        43236\n",
       "open_il_24m                                                        43236\n",
       "mths_since_rcnt_il                                                 43236\n",
       "total_bal_il                                                       43236\n",
       "il_util                                                            43236\n",
       "open_rv_12m                                                        43236\n",
       "open_rv_24m                                                        43236\n",
       "max_bal_bc                                                         43236\n",
       "all_util                                                           43236\n",
       "total_rev_hi_lim                                                       0\n",
       "inq_fi                                                             43236\n",
       "total_cu_tl                                                        43236\n",
       "inq_last_12m                                                       43236\n",
       "emp_length_int                                                         0\n",
       "earliest_cr_line_date                                                  3\n",
       "mths_since_earliest_cr_line                                            0\n",
       "term_int                                                               0\n",
       "issue_d_date                                                           0\n",
       "mths_since_issue_d                                                     0\n",
       "grade:A                                                                0\n",
       "grade:B                                                                0\n",
       "grade:C                                                                0\n",
       "grade:D                                                                0\n",
       "grade:E                                                                0\n",
       "grade:F                                                                0\n",
       "grade:G                                                                0\n",
       "sub_grade:A1                                                           0\n",
       "sub_grade:A2                                                           0\n",
       "sub_grade:A3                                                           0\n",
       "sub_grade:A4                                                           0\n",
       "sub_grade:A5                                                           0\n",
       "sub_grade:B1                                                           0\n",
       "sub_grade:B2                                                           0\n",
       "sub_grade:B3                                                           0\n",
       "sub_grade:B4                                                           0\n",
       "sub_grade:B5                                                           0\n",
       "sub_grade:C1                                                           0\n",
       "sub_grade:C2                                                           0\n",
       "sub_grade:C3                                                           0\n",
       "sub_grade:C4                                                           0\n",
       "sub_grade:C5                                                           0\n",
       "sub_grade:D1                                                           0\n",
       "sub_grade:D2                                                           0\n",
       "sub_grade:D3                                                           0\n",
       "sub_grade:D4                                                           0\n",
       "sub_grade:D5                                                           0\n",
       "sub_grade:E1                                                           0\n",
       "sub_grade:E2                                                           0\n",
       "sub_grade:E3                                                           0\n",
       "sub_grade:E4                                                           0\n",
       "sub_grade:E5                                                           0\n",
       "sub_grade:F1                                                           0\n",
       "sub_grade:F2                                                           0\n",
       "sub_grade:F3                                                           0\n",
       "sub_grade:F4                                                           0\n",
       "sub_grade:F5                                                           0\n",
       "sub_grade:G1                                                           0\n",
       "sub_grade:G2                                                           0\n",
       "sub_grade:G3                                                           0\n",
       "sub_grade:G4                                                           0\n",
       "sub_grade:G5                                                           0\n",
       "home_ownership:ANY                                                     0\n",
       "home_ownership:MORTGAGE                                                0\n",
       "home_ownership:NONE                                                    0\n",
       "home_ownership:OTHER                                                   0\n",
       "home_ownership:OWN                                                     0\n",
       "home_ownership:RENT                                                    0\n",
       "verification_status:Not Verified                                       0\n",
       "verification_status:Source Verified                                    0\n",
       "verification_status:Verified                                           0\n",
       "loan_status:Charged Off                                                0\n",
       "loan_status:Current                                                    0\n",
       "loan_status:Default                                                    0\n",
       "loan_status:Does not meet the credit policy. Status:Charged Off        0\n",
       "loan_status:Does not meet the credit policy. Status:Fully Paid         0\n",
       "loan_status:Fully Paid                                                 0\n",
       "loan_status:In Grace Period                                            0\n",
       "loan_status:Late (16-30 days)                                          0\n",
       "loan_status:Late (31-120 days)                                         0\n",
       "purpose:car                                                            0\n",
       "purpose:credit_card                                                    0\n",
       "purpose:debt_consolidation                                             0\n",
       "purpose:educational                                                    0\n",
       "purpose:home_improvement                                               0\n",
       "purpose:house                                                          0\n",
       "purpose:major_purchase                                                 0\n",
       "purpose:medical                                                        0\n",
       "purpose:moving                                                         0\n",
       "purpose:other                                                          0\n",
       "purpose:renewable_energy                                               0\n",
       "purpose:small_business                                                 0\n",
       "purpose:vacation                                                       0\n",
       "purpose:wedding                                                        0\n",
       "addr_state:AK                                                          0\n",
       "addr_state:AL                                                          0\n",
       "addr_state:AR                                                          0\n",
       "addr_state:AZ                                                          0\n",
       "addr_state:CA                                                          0\n",
       "addr_state:CO                                                          0\n",
       "addr_state:CT                                                          0\n",
       "addr_state:DC                                                          0\n",
       "addr_state:DE                                                          0\n",
       "addr_state:FL                                                          0\n",
       "addr_state:GA                                                          0\n",
       "addr_state:HI                                                          0\n",
       "addr_state:IA                                                          0\n",
       "addr_state:ID                                                          0\n",
       "addr_state:IL                                                          0\n",
       "addr_state:IN                                                          0\n",
       "addr_state:KS                                                          0\n",
       "addr_state:KY                                                          0\n",
       "addr_state:LA                                                          0\n",
       "addr_state:MA                                                          0\n",
       "addr_state:MD                                                          0\n",
       "addr_state:ME                                                          0\n",
       "addr_state:MI                                                          0\n",
       "addr_state:MN                                                          0\n",
       "addr_state:MO                                                          0\n",
       "addr_state:MS                                                          0\n",
       "addr_state:MT                                                          0\n",
       "addr_state:NC                                                          0\n",
       "addr_state:NE                                                          0\n",
       "addr_state:NH                                                          0\n",
       "addr_state:NJ                                                          0\n",
       "addr_state:NM                                                          0\n",
       "addr_state:NV                                                          0\n",
       "addr_state:NY                                                          0\n",
       "addr_state:OH                                                          0\n",
       "addr_state:OK                                                          0\n",
       "addr_state:OR                                                          0\n",
       "addr_state:PA                                                          0\n",
       "addr_state:RI                                                          0\n",
       "addr_state:SC                                                          0\n",
       "addr_state:SD                                                          0\n",
       "addr_state:TN                                                          0\n",
       "addr_state:TX                                                          0\n",
       "addr_state:UT                                                          0\n",
       "addr_state:VA                                                          0\n",
       "addr_state:VT                                                          0\n",
       "addr_state:WA                                                          0\n",
       "addr_state:WI                                                          0\n",
       "addr_state:WV                                                          0\n",
       "addr_state:WY                                                          0\n",
       "initial_list_status:f                                                  0\n",
       "initial_list_status:w                                                  0\n",
       "good_bad                                                               0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_defaults.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Process Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Independent Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda3\\lib\\site-packages\\pandas\\core\\series.py:4517: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  return super().fillna(\n"
     ]
    }
   ],
   "source": [
    "# Fill the missing values with zero\n",
    "loan_data_defaults['mths_since_last_delinq'].fillna(0, inplace = True)\n",
    "loan_data_defaults['mths_since_last_record'].fillna(0, inplace=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Dependent Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-10-7bb2f588252a>:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  loan_data_defaults['recovery_rate'] = \\\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "count    43236.000000\n",
       "mean         0.060820\n",
       "std          0.089770\n",
       "min          0.000000\n",
       "25%          0.000000\n",
       "50%          0.029466\n",
       "75%          0.114044\n",
       "max          1.220774\n",
       "Name: recovery_rate, dtype: float64"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The dependent variable for the LGD model: recovery rate\n",
    "# = the ratio of recoveries and funded amount\n",
    "loan_data_defaults['recovery_rate'] = \\\n",
    "loan_data_defaults['recoveries'] / loan_data_defaults['funded_amnt']\n",
    "loan_data_defaults['recovery_rate'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-11-e2d19d7447e7>:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  loan_data_defaults['recovery_rate'] = \\\n",
      "<ipython-input-11-e2d19d7447e7>:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  loan_data_defaults['recovery_rate'] = \\\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "count    43236.000000\n",
       "mean         0.060770\n",
       "std          0.089202\n",
       "min          0.000000\n",
       "25%          0.000000\n",
       "50%          0.029466\n",
       "75%          0.114044\n",
       "max          1.000000\n",
       "Name: recovery_rate, dtype: float64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Set the rates within [0,1]\n",
    "loan_data_defaults['recovery_rate'] = \\\n",
    "np.where(loan_data_defaults['recovery_rate'] > 1, 1, loan_data_defaults['recovery_rate'])\n",
    "loan_data_defaults['recovery_rate'] = \\\n",
    "np.where(loan_data_defaults['recovery_rate'] < 0, 0, loan_data_defaults['recovery_rate'])\n",
    "loan_data_defaults['recovery_rate'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-12-e8aa4f1cbb05>:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  loan_data_defaults['CCF'] = \\\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "count    43236.000000\n",
       "mean         0.735952\n",
       "std          0.200742\n",
       "min          0.000438\n",
       "25%          0.632088\n",
       "50%          0.789908\n",
       "75%          0.888543\n",
       "max          1.000000\n",
       "Name: CCF, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# The dependent variable for the EAD model: credit conversion factor.\n",
    "# =the ratio of the difference of the amount \n",
    "#  used at the moment of default to the total funded amount.\n",
    "loan_data_defaults['CCF'] = \\\n",
    "(loan_data_defaults['funded_amnt'] - loan_data_defaults['total_rec_prncp'])\\\n",
    "/ loan_data_defaults['funded_amnt']\n",
    "loan_data_defaults['CCF'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_data_defaults.to_csv('loan_data_defaults.csv')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Explore Dependent Variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(loan_data_defaults['recovery_rate'], bins = 50);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(loan_data_defaults['CCF'], bins = 100);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-17-f7724a1bbe90>:2: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  loan_data_defaults['recovery_rate_0_1'] = \\\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1     1\n",
       "8     1\n",
       "9     1\n",
       "12    1\n",
       "14    1\n",
       "Name: recovery_rate_0_1, dtype: int32"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create new variable which is 0 if recovery rate is 0 and 1 otherwise\n",
    "loan_data_defaults['recovery_rate_0_1'] = \\\n",
    "np.where(loan_data_defaults['recovery_rate'] == 0, 0, 1)\n",
    "loan_data_defaults['recovery_rate_0_1'].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. LGD Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Splitting Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_1_train, lgd_inputs_stage_1_test, \\\n",
    "lgd_targets_stage_1_train, lgd_targets_stage_1_test = \\\n",
    "train_test_split(loan_data_defaults.drop(['good_bad', 'recovery_rate',\n",
    "                                          'recovery_rate_0_1', 'CCF'], axis = 1), \n",
    "                 loan_data_defaults['recovery_rate_0_1'], test_size = 0.2, random_state = 42)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Preparing the Inputs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "# List of all independent variables for the models\n",
    "features_all = ['grade:A',\n",
    "'grade:B',\n",
    "'grade:C',\n",
    "'grade:D',\n",
    "'grade:E',\n",
    "'grade:F',\n",
    "'grade:G',\n",
    "'home_ownership:MORTGAGE',\n",
    "'home_ownership:NONE',\n",
    "'home_ownership:OTHER',\n",
    "'home_ownership:OWN',\n",
    "'home_ownership:RENT',\n",
    "'verification_status:Not Verified',\n",
    "'verification_status:Source Verified',\n",
    "'verification_status:Verified',\n",
    "'purpose:car',\n",
    "'purpose:credit_card',\n",
    "'purpose:debt_consolidation',\n",
    "'purpose:educational',\n",
    "'purpose:home_improvement',\n",
    "'purpose:house',\n",
    "'purpose:major_purchase',\n",
    "'purpose:medical',\n",
    "'purpose:moving',\n",
    "'purpose:other',\n",
    "'purpose:renewable_energy',\n",
    "'purpose:small_business',\n",
    "'purpose:vacation',\n",
    "'purpose:wedding',\n",
    "'initial_list_status:f',\n",
    "'initial_list_status:w',\n",
    "'term_int',\n",
    "'emp_length_int',\n",
    "'mths_since_issue_d',\n",
    "'mths_since_earliest_cr_line',\n",
    "'funded_amnt',\n",
    "'int_rate',\n",
    "'installment',\n",
    "'annual_inc',\n",
    "'dti',\n",
    "'delinq_2yrs',\n",
    "'inq_last_6mths',\n",
    "'mths_since_last_delinq',\n",
    "'mths_since_last_record',\n",
    "'open_acc',\n",
    "'pub_rec',\n",
    "'total_acc',\n",
    "'acc_now_delinq',\n",
    "'total_rev_hi_lim']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "# List of the dummy variable reference categories. \n",
    "features_reference_cat = ['grade:G',\n",
    "'home_ownership:RENT',\n",
    "'verification_status:Verified',\n",
    "'purpose:credit_card',\n",
    "'initial_list_status:f']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep only the variabes needed\n",
    "lgd_inputs_stage_1_train = lgd_inputs_stage_1_train[features_all]\n",
    "lgd_inputs_stage_1_train = lgd_inputs_stage_1_train.drop(features_reference_cat, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "grade:A                                0\n",
       "grade:B                                0\n",
       "grade:C                                0\n",
       "grade:D                                0\n",
       "grade:E                                0\n",
       "grade:F                                0\n",
       "home_ownership:MORTGAGE                0\n",
       "home_ownership:NONE                    0\n",
       "home_ownership:OTHER                   0\n",
       "home_ownership:OWN                     0\n",
       "verification_status:Not Verified       0\n",
       "verification_status:Source Verified    0\n",
       "purpose:car                            0\n",
       "purpose:debt_consolidation             0\n",
       "purpose:educational                    0\n",
       "purpose:home_improvement               0\n",
       "purpose:house                          0\n",
       "purpose:major_purchase                 0\n",
       "purpose:medical                        0\n",
       "purpose:moving                         0\n",
       "purpose:other                          0\n",
       "purpose:renewable_energy               0\n",
       "purpose:small_business                 0\n",
       "purpose:vacation                       0\n",
       "purpose:wedding                        0\n",
       "initial_list_status:w                  0\n",
       "term_int                               0\n",
       "emp_length_int                         0\n",
       "mths_since_issue_d                     0\n",
       "mths_since_earliest_cr_line            0\n",
       "funded_amnt                            0\n",
       "int_rate                               0\n",
       "installment                            0\n",
       "annual_inc                             0\n",
       "dti                                    0\n",
       "delinq_2yrs                            0\n",
       "inq_last_6mths                         0\n",
       "mths_since_last_delinq                 0\n",
       "mths_since_last_record                 0\n",
       "open_acc                               0\n",
       "pub_rec                                0\n",
       "total_acc                              0\n",
       "acc_now_delinq                         0\n",
       "total_rev_hi_lim                       0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Check for missing values\n",
    "lgd_inputs_stage_1_train.isnull().sum()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stage 1: Logistic Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Estimating the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# P values for sklearn logistic regression.\n",
    "\n",
    "# Class to display p-values for logistic regression in sklearn.\n",
    "\n",
    "from sklearn import linear_model\n",
    "import scipy.stats as stat\n",
    "\n",
    "class LogisticRegression_with_p_values:\n",
    "    \n",
    "    def __init__(self,*args,**kwargs):#,**kwargs):\n",
    "        self.model = linear_model.LogisticRegression(*args,**kwargs)#,**args)\n",
    "\n",
    "    def fit(self,X,y):\n",
    "        self.model.fit(X,y)\n",
    "        \n",
    "        #### Get p-values for the fitted model ####\n",
    "        denom = (2.0 * (1.0 + np.cosh(self.model.decision_function(X))))\n",
    "        denom = np.tile(denom,(X.shape[1],1)).T\n",
    "        F_ij = np.dot((X / denom).T,X) ## Fisher Information Matrix\n",
    "        Cramer_Rao = np.linalg.inv(F_ij) ## Inverse Information Matrix\n",
    "        sigma_estimates = np.sqrt(np.diagonal(Cramer_Rao))\n",
    "        z_scores = self.model.coef_[0] / sigma_estimates # z-score for eaach model coefficient\n",
    "        p_values = [stat.norm.sf(abs(x)) * 2 for x in z_scores] ### two tailed test for p-values\n",
    "        \n",
    "        self.coef_ = self.model.coef_\n",
    "        self.intercept_ = self.model.intercept_\n",
    "        #self.z_scores = z_scores\n",
    "        self.p_values = p_values\n",
    "        #self.sigma_estimates = sigma_estimates\n",
    "        #self.F_ij = F_ij"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg_lgd_st_1 = LogisticRegression_with_p_values()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda3\\lib\\site-packages\\sklearn\\linear_model\\_logistic.py:762: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    }
   ],
   "source": [
    "reg_lgd_st_1.fit(lgd_inputs_stage_1_train, lgd_targets_stage_1_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "feature_name = lgd_inputs_stage_1_train.columns.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature name</th>\n",
       "      <th>Coefficients</th>\n",
       "      <th>p_values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Intercept</td>\n",
       "      <td>-0.000128</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>grade:A</td>\n",
       "      <td>-0.000016</td>\n",
       "      <td>0.999852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>grade:B</td>\n",
       "      <td>-0.000088</td>\n",
       "      <td>0.998970</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>grade:C</td>\n",
       "      <td>-0.000163</td>\n",
       "      <td>0.998016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>grade:D</td>\n",
       "      <td>0.000019</td>\n",
       "      <td>0.999774</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Feature name  Coefficients  p_values\n",
       "0    Intercept     -0.000128       NaN\n",
       "1      grade:A     -0.000016  0.999852\n",
       "2      grade:B     -0.000088  0.998970\n",
       "3      grade:C     -0.000163  0.998016\n",
       "4      grade:D      0.000019  0.999774"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary_table = pd.DataFrame(columns = ['Feature name'], data = feature_name)\n",
    "summary_table['Coefficients'] = np.transpose(reg_lgd_st_1.coef_)\n",
    "summary_table.index = summary_table.index + 1\n",
    "summary_table.loc[0] = ['Intercept', reg_lgd_st_1.intercept_[0]]\n",
    "summary_table = summary_table.sort_index()\n",
    "p_values = reg_lgd_st_1.p_values\n",
    "p_values = np.append(np.nan,np.array(p_values))\n",
    "summary_table['p_values'] = p_values\n",
    "summary_table.head()\n",
    "\n",
    "#Note: most of the variables aren't statistically significant\n",
    "# throwing them out won't affect the predicting power\n",
    "# but we can keep them to save us effort"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.4 Testing the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep only the needed variables\n",
    "lgd_inputs_stage_1_test = lgd_inputs_stage_1_test[features_all]\n",
    "lgd_inputs_stage_1_test = \\\n",
    "lgd_inputs_stage_1_test.drop(features_reference_cat, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 0, ..., 1, 1, 1])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculates the predicted values for the dependent variable (targets)\n",
    "# based on the values of the independent variables (inputs) supplied as an argument.\n",
    "y_hat_test_lgd_stage_1 = reg_lgd_st_1.model.predict(lgd_inputs_stage_1_test)\n",
    "y_hat_test_lgd_stage_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.41533282, 0.58466718],\n",
       "       [0.38989804, 0.61010196],\n",
       "       [0.51756719, 0.48243281],\n",
       "       ...,\n",
       "       [0.4662346 , 0.5337654 ],\n",
       "       [0.42105712, 0.57894288],\n",
       "       [0.47678806, 0.52321194]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat_test_proba_lgd_stage_1 = reg_lgd_st_1.model.predict_proba(lgd_inputs_stage_1_test)\n",
    "y_hat_test_proba_lgd_stage_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.58466718, 0.61010196, 0.48243281, ..., 0.5337654 , 0.57894288,\n",
       "       0.52321194])"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Take only the probability of recovery rate > 0\n",
    "y_hat_test_proba_lgd_stage_1 = y_hat_test_proba_lgd_stage_1[: ][: , 1]\n",
    "y_hat_test_proba_lgd_stage_1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "178928    1\n",
       "69814     1\n",
       "101396    0\n",
       "463268    1\n",
       "253729    0\n",
       "Name: recovery_rate_0_1, dtype: int32"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgd_targets_stage_1_test_temp = lgd_targets_stage_1_test.copy()\n",
    "lgd_targets_stage_1_test_temp.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    1\n",
       "1    1\n",
       "2    0\n",
       "3    1\n",
       "4    0\n",
       "Name: recovery_rate_0_1, dtype: int32"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lgd_targets_stage_1_test_temp.reset_index(drop = True, inplace = True)\n",
    "lgd_targets_stage_1_test_temp.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>recovery_rate_0_1</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.584667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.610102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0.482433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0.556293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0.401045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   recovery_rate_0_1         0\n",
       "0                  1  0.584667\n",
       "1                  1  0.610102\n",
       "2                  0  0.482433\n",
       "3                  1  0.556293\n",
       "4                  0  0.401045"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_actual_predicted_probs = \\\n",
    "pd.concat([lgd_targets_stage_1_test_temp, pd.DataFrame(y_hat_test_proba_lgd_stage_1)], axis = 1)\n",
    "# Concatenates two dataframes\n",
    "df_actual_predicted_probs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lgd_targets_stage_1_test</th>\n",
       "      <th>y_hat_test_proba_lgd_stage_1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>0.584667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>0.610102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0</td>\n",
       "      <td>0.482433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1</td>\n",
       "      <td>0.556293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0</td>\n",
       "      <td>0.401045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   lgd_targets_stage_1_test  y_hat_test_proba_lgd_stage_1\n",
       "0                         1                      0.584667\n",
       "1                         1                      0.610102\n",
       "2                         0                      0.482433\n",
       "3                         1                      0.556293\n",
       "4                         0                      0.401045"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rename columns\n",
    "df_actual_predicted_probs.columns = \\\n",
    "['lgd_targets_stage_1_test', 'y_hat_test_proba_lgd_stage_1']\n",
    "df_actual_predicted_probs.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lgd_targets_stage_1_test</th>\n",
       "      <th>y_hat_test_proba_lgd_stage_1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>178928</th>\n",
       "      <td>1</td>\n",
       "      <td>0.584667</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69814</th>\n",
       "      <td>1</td>\n",
       "      <td>0.610102</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>101396</th>\n",
       "      <td>0</td>\n",
       "      <td>0.482433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>463268</th>\n",
       "      <td>1</td>\n",
       "      <td>0.556293</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>253729</th>\n",
       "      <td>0</td>\n",
       "      <td>0.401045</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        lgd_targets_stage_1_test  y_hat_test_proba_lgd_stage_1\n",
       "178928                         1                      0.584667\n",
       "69814                          1                      0.610102\n",
       "101396                         0                      0.482433\n",
       "463268                         1                      0.556293\n",
       "253729                         0                      0.401045"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_actual_predicted_probs.index = lgd_inputs_stage_1_test.index\n",
    "df_actual_predicted_probs.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.5 Estimating the accuracy of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "tr = 0.5\n",
    "df_actual_predicted_probs['y_hat_test_lgd_stage_1'] = \\\n",
    "np.where(df_actual_predicted_probs['y_hat_test_proba_lgd_stage_1'] > tr, 1, 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1021</td>\n",
       "      <td>2741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>665</td>\n",
       "      <td>4221</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted     0     1\n",
       "Actual               \n",
       "0          1021  2741\n",
       "1           665  4221"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cf_mtx = pd.crosstab(df_actual_predicted_probs['lgd_targets_stage_1_test'], \n",
    "                     df_actual_predicted_probs['y_hat_test_lgd_stage_1'], \n",
    "                     rownames = ['Actual'], colnames = ['Predicted'])\n",
    "cf_mtx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predicted</th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Actual</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.118062</td>\n",
       "      <td>0.316952</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.076896</td>\n",
       "      <td>0.488090</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predicted         0         1\n",
       "Actual                       \n",
       "0          0.118062  0.316952\n",
       "1          0.076896  0.488090"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cf_mtx_perc = cf_mtx / df_actual_predicted_probs.shape[0]\n",
    "cf_mtx_perc"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6061517113783533"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate Accuracy of the model\n",
    "acc_rate = cf_mtx_perc.iloc[0,0] + cf_mtx_perc.iloc[1,1]\n",
    "acc_rate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import roc_curve, roc_auc_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[array([0.        , 0.        , 0.        , ..., 0.99946837, 0.99946837,\n",
       "        1.        ]),\n",
       " array([0.00000000e+00, 2.04666394e-04, 4.09332788e-04, ...,\n",
       "        9.99795334e-01, 1.00000000e+00, 1.00000000e+00]),\n",
       " array([1.88264835e+00, 8.82648351e-01, 8.63584256e-01, ...,\n",
       "        2.10568544e-01, 1.82003185e-01, 4.56831205e-06])]"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "fpr, tpr, thresholds = \\\n",
    "roc_curve(df_actual_predicted_probs['lgd_targets_stage_1_test'], \n",
    "          df_actual_predicted_probs['y_hat_test_proba_lgd_stage_1'])\n",
    "[fpr, tpr, thresholds]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'ROC curve')"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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EIw6cus2q7ed1tys5l2Rc7wZUdnEwYVV5oygKO3ZsIyhoPqVKldY1o5Mw0E8CQQgBwK34VH47fpN9J/5Go80+P9CtVTU6N6tK2VKFc9rof8XGxjB/fiC//76Xhg29CAycV6yb0RU0gwbC1q1b+eyzz8jKymLkyJEMGzYsx/azZ88ye/ZsMjMzqVixIosXL6Z06dKGLEkI8S9ZGi1/XYpn19FoLt+8p7vf3taKyYMbU7Ni0fl5zG5GN5CsrCwmT57O0KHDJQyeksECITY2lmXLlhEaGoqNjQ2DBw+mZcuWuLm56R4zf/58Jk6cSPv27Vm0aBFff/01kyZNMlRJQoh/Cf09ip8jrulu16telm6tqtGwpml7Cj2t9PTsRXOqV69B//6D6ddvIFWrVjNxVUWTwQIhIiKCVq1a4ejoCIC3tzc7duxgwoQJusdotVpSU1OB7ItFypQpY6hyhBAPnboSzydhZ8jM0mJpoaJXmxp0bVnN4AvSF7SsrCxCQr4lJORbvv9+I+XLl+ftt981dVlFmsECIS4uDhcXF91tV1dXTp06leMx06dPZ/To0SxYsAA7Ozs2bNjwVO9Rrlz+T3C5uJiuva6pyJjNQ25jztJombJyP5ej7+ruWzu3G/YlCu/1A7k5f/487777LidOnKBLly64uJQyu8/aEOM1WCBotdocc5MVRclxOz09HX9/f1avXo2XlxfffPMN06ZNIzg4OM/vkZCQglar6H/gf7i4lDLKGqyFiYzZPDxuzDGJ9wlae5y7KRm6+xaNfR5XRztSk9NJTU43dpn5pigKn322klWrgilVqjQffLCMYcMGEB+fYlafdX7/b1tYqJ74i7TBAqFChQocPXpUd1utVuPq6qq7HRkZia2tLV5eXgAMGjSI5cuXG6ocIczK5Zv3+O2vm/x1KZ70jOxrCEqWsKJfh9q0b1Sp0F9IlhuVSsXff9/C27s7U6a8h6Nj2SI7lsLIYIHQunVrVq5cSWJiInZ2doSHhzN37lzd9urVqxMTE0NUVBS1atVi9+7deHoWv0WrhTCWazFJfLjhJBeuJeqmjQK0ql+ehrWcaN2wogmry7+0tPt89tlKfHz66JrRFfelLE3FYP+q5cuXZ9KkSYwYMYLMzEz69++Pl5cXfn5+TJw4EU9PTxYuXMjbb7+NoiiUK1eOBQsWGKocIYolRVE4dDaGzfuiuJOc3Xa6XGlbGrk509arIpWdHbC2KnwdR/Pq8OE/eP/9Wdy8GY2zswt167pLGBiQSlGUpz8IX0jIOYS8kzEXL4qi8HPENcL2X9Xd16CmE6/28aSMbdGaLfQ4SUlJLFu2mLCwjVSrVp3Zs+fSvHmLxz62OH/OuSly5xCEEAVPqyicuBTPut2XiL+XfTK4ZsXSTBrYCAc762Lz5bhhw1q2bNnMK6+8ytixEyhRooSpSzILEghCFAHJ9zP4Yfcl/jgbq7uvdqXSvDu4CbY2RX+PACAxMYGYmNvUr9+QESNG07ZtOzw86pu6LLMigSBEIbf210h+PXoTAJUK2jWqRJ8XalGmZOFZm/hZKIrC9u1bCQqaT5kyjoSFbcfGxkbCwAQkEIQohBRF4ey1RJauP6m7z69nfVrVL1+splnevv038+YFcvDg73h5NSYwcL70HzIhCQQhCplb8anM+eawbkWy8mXtmP3Kc9jZFq8f16ioK7z88gC0WoWpU2cwaNAwCQMTK17/w4Qowo5ciGP1LxdIe5AFZJ8jGNHVg6quhX8NgqeRnp5OiRIlqFmzFoMHD6Nfv0FUrlzF1GUJJBCEMCmNVsumvVf442ws91KzW0vY2ljydn8v3KuVNXF1BSsrK4vvv1/NmjWrWbt2M+XLl2fixMmmLkv8iwSCECaSkpbJxOX7AbC0UOFWpQyv+tTH1bH4rfd78eIFAgNncP78OTp27IylZdG9WK44k0AQwogys7SEH7nBnuO3dFcW29la8smk9iauzDD+3YyudOkyLF78EZ07exerE+PFid5ASE1NZcmSJURFRbF8+XKWLl3KtGnTKFmypDHqE6JYSLqfwa4j0Ww7dB2A0vbWtKpfHs/a5Xi+QQUTV2c4KpWK27f/pmvXHrz77nQcHYvXYbDiRm8gzJs3D1dXVxISErC1tSUlJYXZs2fz4YcfGqM+IYq0izfu8MVPZ3O0nn7Ow5VxfYrvgu/376fy8cfL6d3bF3d3DwIC5kn/oSJC76d0/vx5Fi5cyL59+7Czs2PJkiX4+PgYozYhiqSov5P441wMEadjuP9wxpBHNUd6t61J3aqOxfpwyaFDB5k7dza3b/9NxYqVcHf3kDAoQvR+UhYWOU/+aDSaR+4Twtz903X0u50XycjUAtmzhRrWdGJAR7diN3X0v5KS7vHhhx+wZUsoNWrUZNWqNTRp0szUZYmnpDcQnnvuORYvXkx6ejr79+8nJCSEFi0e33VQCHNz9EIc3+28SEpapu6+auUdGNDRjQY1nExYmXFt3LiOn3/ewujRr/H6629ga2tr6pJEPuhtf52ZmUlwcDB79+5Fo9Hwwgsv8MYbb2BjY/o+KtL+Ou9kzAUrS6PltcV7dbftba1o36QS3VpWx8HOdGsUG/Nzjo9XExsbQ4MGnmRkZHD1ahTu7h5Gee9/k//beffM7a/37dvHG2+8wRtvvKG778cff6RPnz5PXYwQRZ1Wq/DLn9fZvC8KAGsrC+a92hKXYnjtQG4URWHr1h9ZsmQRjo7/b0ZnijAQBSvXQNizZw9ZWVkEBQWhKAr/7EhkZWWxcuVKCQRhVpJSMwjeepZz1+7o7vOo5sjkwY2xNKNzan//fYt58wKIiDhAo0ZNpBldMZNrIJw/f54//viDhIQEvvvuu/8/wcqKV155xRi1CWFycXfus273ZU5cjgey9wg6NK7MgI61sTKzq23/aUanKDB9+kwGDhwqE0yKmVwD4Z/DRCEhIQwbNsyYNQlRKJyJSmDphuz2085lStCuUSV8WtcwbVEmkJaWhp2dHTVr1mLIkOH06zeQSpUqm7osYQB6zyEMGDCAXbt2kZqaCmRPO71x4waTJk0yeHFCmMK/gwDglW4etGtUyYQVmUZmZibffbeKNWu+Zd26UMqXr8Cbb8rPfXGmNxAmTZpEdHQ0arWa+vXrc/LkSZl2Koqlm3EpbI24xpELcQA0c3ehe6vq1KxY2sSVGd+FC+cICPDn4sXzdO7sjbW16WZOCePJ05XK4eHhBAYGMmrUKLRaLYGBgUYoTQjj+CtSzffhF3XtJSq7lGTwi3XM6jqCfyiKwsqVy/j2268pW9aJDz9cwYsvdjF1WcJI9AaCq6srVlZW1KhRg8jISLp160ZysnnN+RXF0+8n/yZkVySZWdlXFldzdaBvu1p41S5XrNtLPIlKpSI+Xk3Pnn14552plC5dxtQlCSPSGwj29vZs3boVDw8PNmzYQK1atbh//74xahPCIG7EJrPjzxv8cS4WgBebVcGndY1is2j900pNTeHjjz+id+9+eHjUIyBgnkwlNVN654zNnj2b8+fP06ZNGywsLBg+fDhjxowxRm1CFLiNv10m8Jsj/HEulpIlrJg8qDHDXqprtmEQEbGf/v17sW5dCEePHgaQMDBjevcQNm/ezNSpUwH46KOPDF2PEAYRHZfCwjXHSM/QADCxvxeN3ZxNXJXp3Lt3l8WLF/Lzz1uoWbMW33wTQuPGTU1dljAxvYGwd+9eJk+WdU9F0ZSl0bJi0ynOXE0EwNHBhsBRLShtpnsE/9i4cR07dmzDz28cr746VprRCSAPgVClShVGjx5N06ZNc6ySNmrUKIMWJsSz0CoKe49F8+Ha4wBUdi5Jvw61zXqvQK2OIyYmBk9PL0aMGE379h2pU8fd1GWJQkRvIDg6OgJw69YtQ9ciRIGIjL7LopDjuttulcvw3stNzXbmkKIobNkSyocffoCTkxOhoduwsbGRMBCP0BsICxcuNEYdQjyzW/GpzPrqT93t5vXK85pPPbPrOfRvt27d5P33Z/PnnxE0a9ac2bPnykljkSuDrm23detWPvvsM7Kyshg5cuQjPZGioqIICAjg3r17uLi4sHTpUsqUkXnPIu8UReHPc7EEbz2nu69kCSumD2tK4/oVza5P/r9duXKZYcMGYGlpgb9/IP36DZRmdOKJDBYIsbGxLFu2jNDQUGxsbBg8eDAtW7bEzc0NyP5BHjduHP7+/rRr144lS5YQHBzMlClTDFWSKGaOR6r56udzuplD7lUd6dW2JvWqlzVxZaaVlnYfOzt7atWqzYgRo/D1HUCFChVNXZYoAgwWCBEREbRq1Up3DsLb25sdO3YwYcIEAM6ePYu9vT3t2rUDYOzYsSQlJRmqHFGMxCTeZ+aXf6J9uEZHz9Y1aO1ZgfJl7U1cmWllZmayfPlyvvzyK10zuvHjJ5q6LFGE6N1/1Gq1fPXVV0ybNo2UlBS++OILNBqN3heOi4vDxcVFd9vV1ZXY2Fjd7Rs3buDs7MyMGTPo27cvAQEB2Nub9w+0eLIsjZZNe68wI/gPXRhMHtyYvu1qmX0YnDt3hmHD+hMUFESLFq2wtjbvabUif/TuIQQFBZGYmMjp06cB2L9/P2q1mpkzZz7xeVqtNsesDkVRctzOysri8OHDrFmzBk9PTz766CMWLVrEokWL8lz8k9YG1cfFpVS+n1tUFeUxX7udxJtL9upuvzusGe2bVtH7vKI85rxQFIWFCxfy+eef4+zszKpVq/D29jZ1WUZX3D/nxzHEmPUGwqFDhwgLC8PX1xcHBwdWrVpF79699b5whQoVOHr0qO62Wq3G1dVVd9vFxYXq1avj6ekJgI+PDxMnPt3ubUJCClqt8lTPyX5vWZS7qLgek8zHoadISHoAQIMaZXnD15MSNlZ6x1NUx/y0bt68Ta9evkyaNIXatSubxZj/zVw+53/L75gtLFRP/EVabyBYWVnlmJlgY2ODlZX+Uw+tW7dm5cqVJCYmYmdnR3h4OHPnztVtb9KkCYmJiVy4cAEPDw/27NlDgwYN9L6uMB9/x6cyZ/URAFo3rEDPNjXM/tAQQEpKCitWLMXXtz8eHvVlKqkoMHq/2evWrUtISAgajYaoqChWr16Nh4eH3hcuX748kyZNYsSIEWRmZtK/f3+8vLzw8/Nj4sSJeHp68sknnzBz5kzS0tKoUKECQUFBBTIoUfT9cTZGN5W0mbsLr/rUN3FFhcP+/fuYNy8AtTqOmjVr4uFRX8JAFBiVoihPPOaSkpLCggUL2Lt3L1qtlrZt2+Lv70/Zsqaf2ieHjPKuKIz5fnoWvx6NZmvENTQPP9fBndzo0qJavl6vKIw5r+7cucPixQvYvn0rtWvXITBwHp6ejR55XHEac17JmPPumQ8ZxcXFsWDBgqd+YyHySlEUTl5OYMXmU7r7qrk6MKiTG/XMcNWyxwkN3UB4+C+8/vobjBnzOjY2MotIFDy9gfDKK69QtWpVBg4cSLdu3eQ/oihQ/2030aZhBUZ28zDrdhP/iIuLJTY2Bk/PRowYMYr27Tvh5lbH1GWJYixP7a/3799PWFgYixcvpkuXLgwcODBP5xGEyE1GpoY1uyI5cOo2ADUrlubNfp44OkgbZkVRCAvbxNKlQTg5OREWth1raxsJA2FwegPBwsKC9u3b0759e65cucJ7773HDz/8wPnz541RnyiGtv9xnU17r+huj/B2p0OTyiasqPC4eTOa99+fxeHDf9Cs2XOynKUwKr2BkJWVxZ49ewgNDeXUqVN07949x/RRIfJKURTmfXeUq7ezT4Z1bVGNfh1qYSkN14B/mtH1x9LSkpkz5+DrO0Ca0Qmj0hsIbdu2pU6dOvTv358VK1bIOQSRL7GJ93kv+A/d7bmvtqSyc8knPMN8pKamULKkA7Vq1WbkyDH4+g6gfPkKpi5LmCG9gbBu3Tpq1KhhhFJEcXXqSjwfbfz/DKIvp3aQvQIgMzODr78OZt26NfzwQygVK1Zi3Lg3TV2WMGO5BsL8+fPx9/fPtbfQ559/brCiRPGgKArTvziE+m46ABN8PWla10XPs8zD6dOnmDPHn8uXL9Gtmw8lStiZuiQhcg+E559/HsAsG2WJZ3c/PZOFIcd1YbDirRdwsLM2cVWmpygKy5YFsWbNtzg7u7BixWe0a9fR1GUJATwhEDp16gTA9evXefvtt3NsmzdvHn379jVoYaJoytJoWbn5NKejEgCo4uLAey83xc7WoIvzFRkqlYrk5GR8fQfw1lvvUqqU+XXpFIVXrj+lK1asICkpie3bt5OSkqK7PzMzkwMHDuhtfy3MT/zdNKZ+fkh3e3T3erT1kpW6kpOTWbHiQ3x9B1CvXgNmzXpfZg+JQinXQGjUqBGnT5/GwsJCt+oZgKWlJUuWLDFGbaKIuJ+eRejvV9hz/BYAzT1c8fOpj7WVfOnt27eH+fPnEB+vpnZtN+rVayBhIAqtXAPhn4vR2rVrh5eXlzFrEkXItkPX2LwvCgAXxxL0aVuL5xvKlMnExESCguazY8c26tSpy9KlH9OwoaepyxLiifTOMvr0008fu11mGZm3LI2W5ZtOcfZqIgAjurrTobFcbfyPsLCN/PprOOPGvcno0X6ypKUoEmSWkXhqa3dF8uuxm7rbAa88R/UKcnI0NjaG2NgYvLwaM2LEKDp27EytWrVNXZYQeaZ3llHfvn1JSUnBwcGBc+fOERkZSY8ePYxWoChc3vzod1LTswDwaV2dLs9VM/vppFqtltDQDSxbthhnZxddMzoJA1HU6J0LuGLFCq5fv87kyZN59dVXcXNz48iRI8yfP98Y9YlCZN+JW7owWDqhjXQmBa5fv8b778/i2LEjtGz5vMwgEkVantpfh4SEsH79enr06IG/vz++vr7GqE0UIn9Fqvl2x0UA/Ic3kzAguxnd0KH9sLa2ISBgHn369EOlUpm6LCHyLU9XC9nZ2REREcGgQYOA7GsRhHnI0mj5YstZjkWqAXjv5abUrlzGxFWZ1r+b0Y0Z8zp9+vTD1bW8qcsS4pnp3bctW7YsgYGBnDlzhtatW7NkyRJcXV2NUZswsfvpWby2eC/HItVYWVowd0wL6lRxNHVZJpORkcGnn66ge/cXuX37b1QqFa+9Nl7CQBQbevcQPvjgAzZs2EBwcDB2dnaoVCo++OADY9QmTOjIhTg++/EMAC3quTK2d0MTV2Rap06dIDBwJlFRl+nRoxd2dtKMThQ/egPB2dmZ3r17c/jwYc6fP0///v1xdnY2Rm3CBO4kP+C3v27yc8R1AHo8Xx3fdrVMXJXpKIrChx8uIiTkO1xdy7Ny5Re88EJ7U5clhEHoDYT9+/czZcoUmjVrhkajISgoiIULF9K5c2dj1CeMJDNLy3c7LnDwTAwAVV0d6PNCTZrUMe921SqVitTU+/TvP5i33pqMg4ODqUsSwmD0BsLy5ctZs2YNbm5uAFy6dIkpU6ZIIBQjX/18jmORah5kaChhY8mwl+rSxtN8m9IlJSWxbNliBgwYRP36DZk1a45MJRVmQW8gZGZm6sIAoE6dOmg0GoMWJYwjS6NlzjdHuBWfCkCvNjXwaV0DK0vz/fLbs+dXFi6cQ2JiIu7uHtSv31DCQJgNvYFQokQJTp8+jadndmOu06dPywm1YuLdTyNISs3A0kLFZ5Pbm3UQJCTEs2jRPHbt2kHduh4sX/4Z9eub94l0YX70BsKUKVMYO3Ys1atXB+Dq1assX77c4IUJw9FotXz241mSUjNQqSB4Sgezv6Bqy5ZQ9u7dzYQJbzNy5Bisrc27HYcwT3oDoXnz5mzbto2TJ0+i1Wpp3LgxZcuWNUZtwkAmrTxISlr2xYVBY1ubbRjExNwmJuY2jRs3ZfjwV+jUqTM1apjvjCoh9AaCRqNh27ZtHDhwAEtLS+7cuSOtK4qoLI2WxT/8pQuDr6d1NMsw0Gq1bNq0no8+WoyLi6uuGZ2EgTB3egNh3rx5XL58md69e6MoCps2beL69etMmjTJGPWJArQm/CKXbt4D4It3zfMw0fXrV5kzZxbHjx+lVavW0oxOiH/RGwgHDx5k27ZtumOqvXr1olevXhIIRUxSaga/n7wNwFfTOmJhhmFw+fIlhg7th61tCebMWUCvXn3NMhSFyI3eX42cnJxyTDNVqVSULl06Ty++detWunfvTpcuXQgJCcn1cXv37tWtvyAKXlJqBmPmhQPQrlFFswuD5ORkAGrXdsPPbzyhoT/Tu7evhIEQ/6F3D8HDw4OhQ4fi6+uLpaUl27dvp2zZsnzzzTcAjBo16rHPi42NZdmyZYSGhmJjY8PgwYNp2bJljmsaAOLj46U3kgHtPXGL7x62re7xfHX6tTefRVvS09NZuXIZGzb8wPr1YVSqVBk/v7GmLkuIQkvvHsKDBw9wd3fn7NmznDp1iipVqlCuXDkiIyOJjIzM9XkRERG0atUKR0dH7O3t8fb2ZseOHY88bubMmUyYMOHZRiEeoSgKAasO68JgrK+XWYXBiRPH8fb25uuvv6BDh06ULFnS1CUJUejp3UNYuHBhvl44Li4OF5f/98FxdXXl1KlTOR7z3XffUb9+fRo1apSv9yhXLv99ZVxciu8awFqtgt/CX4lLvA9AyPvdKF3SPBZ5VxSFgIAAVq1aReXKlQkJCaFDhw6mLsuoivP/7dzImAtGnhbIyQ+tVpvjGK2iKDluR0ZGEh4ezurVq4mJicnXeyQkpKDVKk/9PBeXUqjVyfl6z8LuZlwKH4edJu5OGna2Vnz89gs8uP8AStoU2zH/1927yQwePIw5c2Zz/77WbMYNxfv/dm5kzHlnYaF64i/SBguEChUqcPToUd1ttVqdY2GdHTt2oFar6devH5mZmcTFxTF06FDWrl1rqJKKvbW7Ivn12E0AmtRx5o2+nmZx4jQp6R5LlwYxYMBgGjTwZObMOahUKkqWLMn9++b1RSHEszDYBOzWrVtz6NAhEhMTSUtLIzw8nHbt2um2T5w4kZ07d7JlyxaCg4NxdXWVMHgGe0/c0oXB2N4NeLOfFxYWxT8Mdu8Ox9fXh61bf+Ts2ewFfcwhBIUwBL2BoNVq+eqrr5g2bRopKSl88cUXeep2Wr58eSZNmsSIESPo06cPPj4+eHl54efnx+nTpwukeJHt6IU43cnjoHHP06Je8V/SMT5ezbvvTmTy5ImUK+dMSMhGBg4cYuqyhCjS9B4yCgoKIjExUfclvn//ftRqNTNnztT74j179qRnz5457vvyyy8feVyVKlXYs2dPXmsW//JXpJpPHy51OaZHPZzLmEcn2p9+CuP33/fy5puTGDFitDSjE6IA6A2EQ4cOERYWhq+vLw4ODqxatYrevXsbozahxx/nYgj+6RwAb/T1pJl78V7d7Natm8TFxdGkSVOGDx/Fiy92oXr1GqYuS4hiQ+8hIysrqxy9XmxsbLCyMti5aJFHiqKwatsFAEZ18yjWYaDVavnhh+/p378Xc+b4o9Vqsba2ljAQooDp/WavW7cuISEhaDQaoqKiWL16NR4eHsaoTTzBjsM3yNJoaVDTiRcaVTJ1OQZz9WoUgYH+nDz5F23avIC/f6A0oxPCQPT+ZPn7+3P27FkSEhIYMmQIqampzJgxwxi1iVxotFo2/nYFO1tLxvcpvqt6Xb58iUGD+nDtWhTz5n3Axx8HU6lSZVOXJUSxpXcPwcHBgQULFhijFpEHiqIw+ZMIAF5sVhU72+J3+C4pKYnSpUtTu7YbY8dOoHdvX8qVczZ1WUIUe3laD+Fx8jLLSBSse6kZTFp5QHe77ws1TVhNwUtPTyc4+BM2blyva0Y3evRrpi5LCLOh95CRo6Oj7k/JkiU5fPiwMeoS/3E7IVUXBjUrlubzye2L1QVYf/11jEGD+rBq1Ze8+OJLODjkv0+VECJ/9O4h/LcTqZ+fH+PGjTNYQeLxFq45DoBX7XK8PSB/zQALI0VR+OCDeaxbF0KlSpX5/PNVtGrV2tRlCWGWnvoAtIODA3FxcYaoReTio40nSUnLpEU9V8b2Ll4nkVUqFRqNhqFDRzBhwlvY20ubaiFMRW8gzJ07V3doQlEUzp49S61ashi5sYSER3LqSgKWFirG9Khv6nIKxN27d/jwww8YNGgYDRt6MmNGQLE6/CVEUaU3EMqWLZvj9j9rKgvD23boGruPZzesW/HWC1hbFe3594qisGvXThYtmktS0j28vBrTsKF5dGQVoijQGwg3btwgKCjIGLWIf7l6O4nN+6IAmDG8WZGfXqpWx7Fgwfv89tuv1K/fgM8++xp3d7nAUYjCRO+3zIULFx5Z3EYY1p3kB8z9NnstifF9GuJWuYyJK3p2P/+8hYiI/bz99hRefnmktD8RohDS+1Pp4uJCjx49aNSoUY51aeU6BMM4dy2RJetOANCuUSWae7g++QmF2K1bN4mNjaFp0+a8/PIrdO7sTdWq1UxdlhAiF7kGQkZGBjY2NjRp0oQmTZoYsyaztWr7eQ6cug1An7Y16dW2aF54ptFoWLcuhJUrl1GhQgVCQ7dhbW0tYSBEIZdrIAwaNIiwsLBHrkMQhnHkQpwuDAJHPUe18kVz0fArVy4zZ85MTp06QZs27Zg1a440oxOiiMg1EBTl6RevF/mTpdHy2cNFbt4f3YIqrkXzKt3LlyMZMqQfJUuWZP78xXTv7iPnnoQoQnINhAcPHnDu3Llcg6FBgwYGK8rcvL/6CAD1qpctkmGQlHSP0qXLULt2HcaPf4vevfvi5FTO1GUJIZ5SroEQHR3Nm2+++dhAUKlU7N6926CFmQONVsvqXy5wU50KwFv9vUxc0dNJT0/n888/ZtOm7GZ0lStXYdSoV01dlhAin3INBDc3N3788UcjlmJeku9n8OH6E9yITQFgvl9LbKwtTVxV3h09epg5c2YRHX2dvn0HUKpUaVOXJIR4RjIZ3AQio++yKCS7WZ1zmRIseK0VVpZF48SrVqtl4cK5bNz4A1WqVCU4eDUtWrQydVlCiAKQayA0b97cmHWYlSXr/gKgc7MqDO5cB4sidOL1nxlDI0aMYty4idjZ2Zm4IiFEQck1EOTCs4J3N+UBn285S5ZGwblMCYa+VNfUJeXJnTt3WLJkIUOGDH/YjG62zB4SohgqGscpiolZX/1JZPRd7GytmDqk8F/spygKO3Zsw9e3Ozt3/sLFi+cBJAyEKKbkHIKRxN9LIzU9i9qVS+M/vPAfjouNjWXhwjns3buHBg08CQycR5067qYuSwhhQBIIRnAn+QEBq7KXHvV9oWisJbF9+0/88UcE77wzlWHDRmJpWXRmQAkh8kcCwcA0Wi2TPzkIQL/2tahXw8nEFeUuOvoGanWcrhndSy91pUqVqqYuSwhhJHIOwcAWr82eUdSwlhM9nq9h2mJyodFo+P77bxgwoBdz585Gq9VibW0tYSCEmZE9BAOKv5tG5M17AEwa0MjE1Tze5cuRBAbO5MyZU7Rr1wF//0BpRieEmZJAMJAsjZb3Hy5y81qv+oVyZs7ly5EMHtyPUqUcWLToQ7y9uxfKOoUQxmHQXwW3bt1K9+7d6dKlCyEhIY9s//XXX+nduze9evVi/Pjx3Lt3z5DlGFXEmRhS0jJp16girepXMHU5Ody9eweA2rXrMHHiJEJDt9O1aw8JAyHMnMECITY2lmXLlrF27Vp+/PFH1q9fz+XLl3XbU1JSCAwMJDg4mJ9++gl3d3dWrlxpqHKMKv5uGqt/uQDAgI5uJq7m/9LS0vjww0X06NGZW7duolKpGDFiNGXLljV1aUKIQsBggRAREUGrVq1wdHTE3t4eb29vduzYoduemZlJQEAA5cuXB8Dd3Z3bt28bqhyjSXuQxdTPDwHQ4/nqlCxhbeKKsh08eJABA3rx/fer6dbNh9Kli/46zUKIgmWwcwhxcXG4uLjobru6unLq1Cnd7bJly/LSSy8B2W2Ug4ODGT58uKHKMZrN+64A0KZhBfq1r23iarKb0S1YMIdNm9ZTtWo1vvzyW557rqWpyxJCFEIGCwStVpvjmLSiKI89Rp2cnMwbb7yBh4cHffv2far3KFcu/4vJuLgYZonKPcdvATB9VOH50nVwsGPcuHFMnjzZ7JrRGepzLsxkzObBEGM2WCBUqFCBo0eP6m6r1WpcXV1zPCYuLo4xY8bQqlUrZsyY8dTvkZCQglb79Et9uriUQq1Ofurn6XP0QhwADWs6GeT18yoxMZHFixcwdOhwPD0b8dZb03B1LY1anUxKiunqMjZDfc6FmYzZPOR3zBYWqif+Im2wcwitW7fm0KFDJCYmkpaWRnh4OO3atdNt12g0jB07lm7duuHv71/kZ7hkabR8+nBdZFMdKlIUhe3bt+Lr251du3Zy6VIkIM3ohBB5Y7A9hPLlyzNp0iRGjBhBZmYm/fv3x8vLCz8/PyZOnEhMTAznzp1Do9Gwc+dOABo2bMj8+fMNVZJBbfwt+9xBrzY1qF7B+LuvMTG3mT8/kP379+Hp2YiAgHm4udUxeh1CiKLLoBem9ezZk549e+a478svvwTA09OTCxcuGPLtjUZRFHYdjQbAp3UNk9Twyy/bOHLkMO+++x5DhrwszeiEEE9NrlQuABFnYgB4qXlVoy6Fef36NdTqOJo3b8HLL4+kS5euVK5cxWjvL4QoXiQQnlFKWiZfb8teOKZzc+N8GWdlZbFmzbd89tkKKlWqzObNP2NtbS1hIIR4JhIIz2jjb9lXXw/pXAcXR8NP6YyMvEhgoD/nzp2hQ4cXmTFjtjSjE0IUCAmEZ7B+zyX2n7qNW+UyvNjU8L+dX7p0kaFD+1G6dBmCgj7ipZe8ZQaREKLASCDk0824FHYezj6RPH1YUywsDPfFfOfOHcqWLYubW13eemsyPXv2wdFR+g8JIQqWHGvIhyyNltkPl8R8o29Dg4VBWtp9Fi9eiI/P/5vRDR8+SsJACGEQsoeQD9MeNq+r4GRPM3dXPY/Onz/+iOD992fx99+3GDhwKGXKOBrkfYQQ4h8SCE8pOi6FO8kPAJj7aosCf32tVsvcubMJC9tEtWrV+frr72nW7LkCfx8hhPgvCYSn8CBTQ8DDQ0UzXm6GpQFm91hYWFCiRAlGjfLj9dffoESJEgX+HkII8TgSCE8hZFd2b6AaFUrhVqXg1hNISIgnKGgBw4aNwMurMVOnFv3eTkKIokdOKj+Fk5fjAZg1snmBvJ6iKPz88xZ8fXuwZ88uoqKy+yFJGAghTEH2EPLodkIqyfczaVS7XIF8Yd++/Tfz5gVy8ODvNGrUhMDA+dSsWasAKhVCiPyRQMijX/64AUDHAroAbefOXzh+/CjTpvkzaNAwudpYCGFyEgh5EHc3jQOns9d7bljTKd+vc/36VeLi4njuuZa8/PJIvL27UbFipYIqUwghnon8WpoHW/ZfBaBf+1r5uggtKyuLb775kgEDerNw4ftotVqsrKwkDIQQhYrsIegRdzeNQ2ez21t3a1n9qZ9/8eIFAgNncP78OV588SXee0+a0QkhCicJBD1Wb89ubZ2fvYNLly4ybFh/ypRxZMmS5XTu7G2IEoUQokBIIDyBoihcuHEXgO6t8r53kJiYiJOTE25udZk0aSo+Pr2k9YQQotCTYxdPsG539loHHZtWztNU0/v3U/ngg3n4+HTm5s1oVCoVw4aNkDAQQhQJsoeQiyyNVrdO8qCObnofHxFxgLlzZxMTc5vBg4fh5JT/2UhCCGEKEgi5mLTyAABN67pgY537gvVarZY5c2ayZUsoNWrUZNWqEJo0aWqsMoUQosBIIDzG/pN/k5qeBcD4vg2f+FgLCwvs7UsyZszrvPbaeGxtbY1RohBCFDgJhMcI2x8FwLI322LxmHMH8fFqPvhgPi+/PJJGjZowdeoM6T8khCjy5KTyf/x+8m/upmTgUc2RMiVtcmxTFIUtW0Lx9fVh3749XL2aHRwSBkKI4kD2EP4lI1PD6l8uAPBK93o5tt26dZN58wI4dOggTZo0IyBgLjVqSDM6IUTxIYHwL1/9fA7IvubA1dEux7Zdu3Zy8uRfvPfebAYMGCxXGwshih0JhIcu3bzL0YtqAPp3qA3A1atRqNVxtGjRipdfHknXrt2pUKGiKcsUQgiDkV9zAY1Wy8I1xwEY3b0emZmZfPXV5wwc2JtFi+bpmtFJGAghijPZQwDdeYO6VcpQzjqRYcPGERl5gS5dujFtmr8cHhJCmAWzD4SfI65x8HR2N9PujWx5+eWBlC3rxNKlH9OpU2cTVyeEEMZj1oFw9EIcob9HkZmexLK3vSlXpgTvvjudHj16Ubp0GVOXJ4QQRmXQYyFbt26le/fudOnShZCQkEe2nz9/Hl9fX7y9vfH39ycrK8uQ5eRw6ko8KzceJfrYeiJ/CSQtWY1KpWLIkOESBkIIs2SwQIiNjWXZsmWsXbuWH3/8kfXr13P58uUcj5kyZQqzZ89m586dKIrChg0bDFVODgn30piz/AfO/TKX+Mu/07//IJydnY3y3kIIUVgZLBAiIiJo1aoVjo6O2Nvb4+3tzY4dO3Tbb926RXp6Oo0bNwbA19c3x3ZDSUxKo5PPcK78/gllSjmwevVapkx5Dzs7e4O/txBCFGYGO4cQFxeHi4uL7rarqyunTp3KdbuLiwuxsbFP9R7lyjk8dV3RCWlYWNvh028kKxYHmFUzOheXUqYuwehkzOZBxlwwDBYIWq02R48fRVFy3Na3PS8SElLQapWnek7VcnYcDv+Wu3dSSUrKADKe6vlFlYtLKdTqZFOXYVQyZvMgY847CwvVE3+RNtghowoVKqBWq3W31Wo1rq6uuW6Pj4/Psd2QrK3kugIhhPgvg30ztm7dmkOHDpGYmEhaWhrh4eG0a9dOt71y5crY2tpy7NgxALZs2ZJjuxBCCOMyWCCUL1+eSZMmMWLECPr06YOPjw9eXl74+flx+vRpAJYsWcLChQvp2rUr9+/fZ8SIEYYqRwghhB4qRVGe7iB8IZKfcwggxxzNhYzZPMiY885k5xCEEEIULRIIQgghAAkEIYQQDxXp5nYWFvlfy/hZnltUyZjNg4zZPORnzPqeU6RPKgshhCg4cshICCEEIIEghBDiIQkEIYQQgASCEEKIhyQQhBBCABIIQgghHpJAEEIIAUggCCGEeEgCQQghBFDMA2Hr1q10796dLl26EBIS8sj28+fP4+vri7e3N/7+/mRlZZmgyoKlb8y//vorvXv3plevXowfP5579+6ZoMqCpW/M/9i7dy+dOnUyYmWGo2/MUVFRDB8+nF69ejFmzBiz+JzPnj1Lv3796NWrF6+//jpJSUkmqLJgpaSk4OPjw82bNx/ZZpDvL6WYiomJUTp27KjcuXNHSU1NVXr27KlcunQpx2N69Oih/PXXX4qiKMp7772nhISEmKDSgqNvzMnJyUqbNm2UmJgYRVEU5aOPPlLmzp1rqnILRF4+Z0VRFLVarXTt2lXp2LGjCaosWPrGrNVqlS5duij79u1TFEVRFi9erAQFBZmq3AKRl895yJAhyt69exVFUZSFCxcqS5cuNUWpBebEiROKj4+P0qBBAyU6OvqR7Yb4/iq2ewgRERG0atUKR0dH7O3t8fb2ZseOHbrtt27dIj09ncaNGwPg6+ubY3tRpG/MmZmZBAQEUL58eQDc3d25ffu2qcotEPrG/I+ZM2cyYcIEE1RY8PSN+ezZs9jb2+uWpB07dizDhg0zVbkFIi+fs1arJTU1FYC0tDRKlChhilILzIYNGwgICHjsWvOG+v4qtoEQFxeHi4uL7rarqyuxsbG5bndxccmxvSjSN+ayZcvy0ksvAZCenk5wcDCdO3c2ep0FSd+YAb777jvq169Po0aNjF2eQegb840bN3B2dmbGjBn07duXgIAA7O3tTVFqgcnL5zx9+nRmzpxJ27ZtiYiIYPDgwcYus0DNnz+f5s2bP3abob6/im0gaLVaVKr/t3pVFCXHbX3bi6K8jik5OZnXXnsNDw8P+vbta8wSC5y+MUdGRhIeHs748eNNUZ5B6BtzVlYWhw8fZsiQIYSFhVG1alUWLVpkilILjL4xp6en4+/vz+rVqzlw4ABDhw5l2rRppijVKAz1/VVsA6FChQqo1WrdbbVanWPX67/b4+PjH7trVpToGzNk/2YxdOhQ3N3dmT9/vrFLLHD6xrxjxw7UajX9+vXjtdde042/KNM3ZhcXF6pXr46npycAPj4+nDp1yuh1FiR9Y46MjMTW1hYvLy8ABg0axOHDh41ep7EY6vur2AZC69atOXToEImJiaSlpREeHq47pgpQuXJlbG1tOXbsGABbtmzJsb0o0jdmjUbD2LFj6datG/7+/kV+jwj0j3nixIns3LmTLVu2EBwcjKurK2vXrjVhxc9O35ibNGlCYmIiFy5cAGDPnj00aNDAVOUWCH1jrl69OjExMURFRQGwe/duXSAWRwb7/nrm09KF2E8//aT06NFD6dKlixIcHKwoiqK8+uqryqlTpxRFUZTz588r/fr1U7y9vZV33nlHefDggSnLLRBPGnN4eLji7u6u9OrVS/dnxowZJq742en7nP8RHR1dLGYZKYr+MZ84cULp16+f0r17d2X06NFKfHy8KcstEPrGvHfvXqVnz56Kj4+PMnLkSOXGjRumLLfAdOzYUTfLyNDfX7JimhBCCKAYHzISQgjxdCQQhBBCABIIQgghHpJAEEIIAUggCCGEeEgCQRRK7u7u9OzZk969e+v++Pv7P/E5oaGhvP7660aqMO92797NvHnzgOyOq8uXL3/kfmP6+OOP+fXXX43+vqLwszJ1AULk5ttvv8XJycnUZTyzF198kRdffBGA06dP61pR//t+Y/rzzz9xc3Mz+vuKwk8CQRQ5mzZtYv369WRmZnLv3j38/PweaUcRHh7OZ599hkqlwtLSkqlTp/Lcc8+RnJzM/PnziYyMJDMzk+eff56pU6diZZXzR2H69OnY2tpy4cIFEhISaNOmDTNnzsTa2pqjR48SFBREWloa1tbWvP3227Rr1w61Ws20adO4c+cOAO3bt+ftt98mNDSUnTt3Mn78eNatW4dGo6FUqVJUr16dnTt3Mn36dAYPHsz+/fuxsbFBo9HQoUMHVq9ejaura57rvXv3LtHR0XTo0IH+/fvz/vvvk5qailqtxsPDg48++ohNmzZx5swZgoKCsLS0pH379ixZsoQjR46g0WioX78+M2fOxMHBwbAfoiiU5JCRKLRGjhyZ45BRQkICqampbNy4keDgYH788UeWLVvG4sWLH3luUFAQAQEBhIaG8tZbb/Hnn38CsGDBAho0aEBoaCg//vgjd+7c4Ztvvnns+586dYpVq1axfft2rly5wvr167lz5w4TJ07E39+frVu38sEHHzBlyhSio6PZsGEDVapUISwsjJCQEK5fv05ycrLu9Ro1asTgwYPp3r07kyZN0t1fs2ZN6tSpw549ewA4cOAAVapUoXbt2k9Vb3p6Otu2bWPKlCls2LCBPn36sGHDBsLDw7l58yZ79+5l2LBhNGzYkKlTp/LSSy8RHByMpaUloaGh/PTTT7i6urJkyZJ8f2aiaJM9BFFo5XbI6PPPP2ffvn1cu3aNCxcucP/+/Uce06NHDyZMmED79u1p06YNfn5+QPYx/NOnT7Np0yYg+0s0N3379qVkyZIA9O7dm927d1O1alWqVauma6Vdp04dmjZtyuHDh3nhhRd47bXXuH37Nq1bt2by5MmUKlUqT2Pt378/YWFhdO3aldDQUAYOHPjU9TZr1kz39ylTpnDw4EG+/PJLrl27Rlxc3GP/nfbu3UtycjIRERFA9poZ5cqVy1PNoviRQBBFSkxMDIMGDWLgwIE0a9aMrl278ttvvz3yuEmTJtGvXz8OHjxIaGgoq1atYtOmTWi1WpYvX07t2rUBSEpKyrXJn6Wlpe7viqJgYWGBRqN55PGKopCVlYWXlxe7d+/m0KFD/PHHHwwYMIAvv/wyT+Pq1q0bixYt4sqVKxw5ckTXrvpp6v33mgfvvPMOGo2Gbt260aFDB27fvs3jutRotVpmzJhB+/btAUhNTeXBgwd5qlkUP3LISBQpZ86cwcnJifHjx9O2bVtdGGg0Gt1jsrKy6NSpE2lpaQwZMoSAgAAuXrxIRkYGbdu2ZfXq1SiKQkZGBuPGjWPNmjWPfa9ffvmFjIwMHjx4QFhYGB07dqRx48ZERUXp2klfunSJI0eO0KJFC5YsWcKnn35K586d8ff3x83NjUuXLuV4TUtLy8eufWtra0uPHj2YPn06Xbp0wc7ODuCp6v23AwcO8MYbb9C9e3cATp48qfs3+ncNbdu2JSQkhIyMDLRaLbNmzWLp0qV6X18UT7KHIIqUNm3asGnTJrp27YpKpaJFixY4OTlx/fp13WOsrKyYMWMG7777LlZWVqhUKhYsWICNjQ3+/v7Mnz+fnj17kpmZSevWrXn11Vcf+14lSpRg6NChJCUl4e3tTb9+/bCwsGD58uXMnTuX9PR0VCoVCxcupGbNmowcOZLp06fj4+ODjY0N7u7u9OjRg59//ln3mq1ateLdd99l7ty5j7SkHjBgAGvWrCEwMFB339PU+2+TJk3ijTfewN7eHgcHB5577jlu3LgBQKdOnVi6dCmZmZmMHz+eDz74gL59+6LRaKhXrx7Tp09/mo9EFCPS7VSIx5g+fTp16tRhzJgxpi5FCKORQ0ZCCCEA2UMQQgjxkOwhCCGEACQQhBBCPCSBIIQQApBAEEII8ZAEghBCCEACQQghxEP/A+cCN3/a1adhAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(fpr, tpr)\n",
    "plt.plot(fpr, fpr, linestyle = '--', color = 'k')\n",
    "plt.xlabel('False positive rate')\n",
    "plt.ylabel('True positive rate')\n",
    "plt.title('ROC curve')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6511244247633932"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "AUROC = roc_auc_score(df_actual_predicted_probs['lgd_targets_stage_1_test'], \n",
    "                      df_actual_predicted_probs['y_hat_test_proba_lgd_stage_1'])\n",
    "AUROC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save the Model\n",
    "import pickle\n",
    "pickle.dump(reg_lgd_st_1, open('lgd_model_stage_1.sav', 'wb'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Stage 2: Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.6 Estimating the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_stage_2_data = \\\n",
    "loan_data_defaults[loan_data_defaults['recovery_rate_0_1'] == 1]\n",
    "# Only rows where the original recovery rate variable is greater than one"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# LGD model stage 2 datasets: how much more than 0 is the recovery rate\n",
    "lgd_inputs_stage_2_train, lgd_inputs_stage_2_test, \\\n",
    "lgd_targets_stage_2_train, lgd_targets_stage_2_test = \\\n",
    "train_test_split(lgd_stage_2_data.drop(['good_bad', 'recovery_rate',\n",
    "                                        'recovery_rate_0_1', 'CCF'], axis = 1), \n",
    "                 lgd_stage_2_data['recovery_rate'], test_size = 0.2, random_state = 42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn import linear_model\n",
    "from sklearn.metrics import mean_squared_error, r2_score"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Since the p-values are obtained through certain statistics, we need the 'stat' module from scipy.stats\n",
    "import scipy.stats as stat\n",
    "\n",
    "# Since we are using an object oriented language such as Python, we can simply define our own \n",
    "# LinearRegression class (the same one from sklearn)\n",
    "# By typing the code below we will ovewrite a part of the class with one that includes p-values\n",
    "# Here's the full source code of the ORIGINAL class: https://github.com/scikit-learn/scikit-learn/blob/7b136e9/sklearn/linear_model/base.py#L362\n",
    "\n",
    "\n",
    "class LinearRegression(linear_model.LinearRegression):\n",
    "    \"\"\"\n",
    "    LinearRegression class after sklearn's, but calculate t-statistics\n",
    "    and p-values for model coefficients (betas).\n",
    "    Additional attributes available after .fit()\n",
    "    are `t` and `p` which are of the shape (y.shape[1], X.shape[1])\n",
    "    which is (n_features, n_coefs)\n",
    "    This class sets the intercept to 0 by default, since usually we include it\n",
    "    in X.\n",
    "    \"\"\"\n",
    "    \n",
    "    # nothing changes in __init__\n",
    "    def __init__(self, fit_intercept=True, normalize=False, copy_X=True,\n",
    "                 n_jobs=1):\n",
    "        self.fit_intercept = fit_intercept\n",
    "        self.normalize = normalize\n",
    "        self.copy_X = copy_X\n",
    "        self.n_jobs = n_jobs\n",
    "\n",
    "    \n",
    "    def fit(self, X, y, n_jobs=1):\n",
    "        self = super(LinearRegression, self).fit(X, y, n_jobs)\n",
    "        \n",
    "        # Calculate SSE (sum of squared errors)\n",
    "        # and SE (standard error)\n",
    "        sse = np.sum((self.predict(X) - y) ** 2, axis=0) / float(X.shape[0] - X.shape[1])\n",
    "        se = np.array([np.sqrt(np.diagonal(sse * np.linalg.inv(np.dot(X.T, X))))])\n",
    "\n",
    "        # compute the t-statistic for each feature\n",
    "        self.t = self.coef_ / se\n",
    "        # find the p-value for each feature\n",
    "        self.p = np.squeeze(2 * (1 - stat.t.cdf(np.abs(self.t), y.shape[0] - X.shape[1])))\n",
    "        return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.stats as stat\n",
    "\n",
    "class LinearRegression(linear_model.LinearRegression):\n",
    "    def __init__(self, fit_intercept=True, normalize=False, copy_X=True,\n",
    "                 n_jobs=1):\n",
    "        self.fit_intercept = fit_intercept\n",
    "        self.normalize = normalize\n",
    "        self.copy_X = copy_X\n",
    "        self.n_jobs = n_jobs\n",
    "    def fit(self, X, y, n_jobs=1):\n",
    "        self = super(LinearRegression, self).fit(X, y, n_jobs)\n",
    "        sse = np.sum((self.predict(X) - y) ** 2, axis=0) / float(X.shape[0] - X.shape[1])\n",
    "        se = np.array([np.sqrt(np.diagonal(sse * np.linalg.inv(np.dot(X.T, X))))])\n",
    "        self.t = self.coef_ / se\n",
    "        self.p = np.squeeze(2 * (1 - stat.t.cdf(np.abs(self.t), y.shape[0] - X.shape[1])))\n",
    "        return self"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep the needed variables\n",
    "lgd_inputs_stage_2_train = lgd_inputs_stage_2_train[features_all]\n",
    "lgd_inputs_stage_2_train = lgd_inputs_stage_2_train.drop(features_reference_cat, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_lgd_st_2 = LinearRegression()\n",
    "reg_lgd_st_2.fit(lgd_inputs_stage_2_train, lgd_targets_stage_2_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature name</th>\n",
       "      <th>Coefficients</th>\n",
       "      <th>p_values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Intercept</td>\n",
       "      <td>0.240686</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>grade:A</td>\n",
       "      <td>-0.068269</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>grade:B</td>\n",
       "      <td>-0.050836</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>grade:C</td>\n",
       "      <td>-0.037481</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>grade:D</td>\n",
       "      <td>-0.027173</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Feature name  Coefficients  p_values\n",
       "0    Intercept      0.240686       NaN\n",
       "1      grade:A     -0.068269       0.0\n",
       "2      grade:B     -0.050836       0.0\n",
       "3      grade:C     -0.037481       0.0\n",
       "4      grade:D     -0.027173       0.0"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_name = lgd_inputs_stage_2_train.columns.values\n",
    "summary_table = pd.DataFrame(columns = ['Feature name'], data = feature_name)\n",
    "summary_table['Coefficients'] = np.transpose(reg_lgd_st_2.coef_)\n",
    "summary_table.index = summary_table.index + 1\n",
    "summary_table.loc[0] = ['Intercept', reg_lgd_st_2.intercept_]\n",
    "summary_table = summary_table.sort_index()\n",
    "p_values = reg_lgd_st_2.p\n",
    "p_values = np.append(np.nan,np.array(p_values))\n",
    "summary_table['p_values'] = p_values.round(3)\n",
    "summary_table.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.7 Model Evaluation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_inputs_stage_2_test = lgd_inputs_stage_2_test[features_all]\n",
    "lgd_inputs_stage_2_test = lgd_inputs_stage_2_test.drop(features_reference_cat, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_lgd_stage_2 = reg_lgd_st_2.predict(lgd_inputs_stage_2_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_targets_stage_2_test_temp = lgd_targets_stage_2_test.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [],
   "source": [
    "lgd_targets_stage_2_test_temp = \\\n",
    "lgd_targets_stage_2_test_temp.reset_index(drop = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>recovery_rate</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>recovery_rate</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.307996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.307996</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               recovery_rate         0\n",
       "recovery_rate       1.000000  0.307996\n",
       "0                   0.307996  1.000000"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the correlation between actual and predicted values.\n",
    "pd.concat([lgd_targets_stage_2_test_temp, pd.DataFrame(y_hat_test_lgd_stage_2)], axis = 1).corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='recovery_rate', ylabel='Density'>"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the distribution of the residuals.\n",
    "sns.distplot(lgd_targets_stage_2_test - y_hat_test_lgd_stage_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save the model\n",
    "pickle.dump(reg_lgd_st_2, open('lgd_model_stage_2.sav', 'wb'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.8 Combining Stage 1 and Stage 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Include all records\n",
    "y_hat_test_lgd_stage_2_all = reg_lgd_st_2.predict(lgd_inputs_stage_1_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.1193906 , 0.09605635, 0.        , ..., 0.12078611, 0.11587422,\n",
       "       0.15667447])"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat_test_lgd = y_hat_test_lgd_stage_1 * y_hat_test_lgd_stage_2_all\n",
    "# Combine the predictions of the models from the two stages\n",
    "y_hat_test_lgd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8648.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.086777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.049741</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>-0.007634</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.064223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.100906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.122950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.236973</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count  8648.000000\n",
       "mean      0.086777\n",
       "std       0.049741\n",
       "min      -0.007634\n",
       "25%       0.064223\n",
       "50%       0.100906\n",
       "75%       0.122950\n",
       "max       0.236973"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(y_hat_test_lgd).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
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       "  </thead>\n",
       "  <tbody>\n",
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       "      <th>count</th>\n",
       "      <td>8648.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.086779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.049737</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.064223</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.100906</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.122950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.236973</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count  8648.000000\n",
       "mean      0.086779\n",
       "std       0.049737\n",
       "min       0.000000\n",
       "25%       0.064223\n",
       "50%       0.100906\n",
       "75%       0.122950\n",
       "max       0.236973"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat_test_lgd = np.where(y_hat_test_lgd < 0, 0, y_hat_test_lgd)\n",
    "y_hat_test_lgd = np.where(y_hat_test_lgd > 1, 1, y_hat_test_lgd)\n",
    "pd.DataFrame(y_hat_test_lgd).describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. EAD Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1 Estimation and Interpretation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_inputs_train, ead_inputs_test, ead_targets_train, ead_targets_test = \\\n",
    "train_test_split(loan_data_defaults.drop(['good_bad', 'recovery_rate',\n",
    "                                          'recovery_rate_0_1', 'CCF'], axis = 1), \n",
    "                 loan_data_defaults['CCF'], test_size = 0.2, random_state = 42)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_inputs_train = ead_inputs_train[features_all]\n",
    "ead_inputs_train = ead_inputs_train.drop(features_reference_cat, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LinearRegression()"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "reg_ead = LinearRegression()\n",
    "reg_ead.fit(ead_inputs_train, ead_targets_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Feature name</th>\n",
       "      <th>Coefficients</th>\n",
       "      <th>p_values</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Intercept</td>\n",
       "      <td>1.109746</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>grade:A</td>\n",
       "      <td>-0.303003</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>grade:B</td>\n",
       "      <td>-0.236428</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>grade:C</td>\n",
       "      <td>-0.172023</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>grade:D</td>\n",
       "      <td>-0.119847</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Feature name  Coefficients  p_values\n",
       "0    Intercept      1.109746       NaN\n",
       "1      grade:A     -0.303003       0.0\n",
       "2      grade:B     -0.236428       0.0\n",
       "3      grade:C     -0.172023       0.0\n",
       "4      grade:D     -0.119847       0.0"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "feature_name = ead_inputs_train.columns.values\n",
    "summary_table = pd.DataFrame(columns = ['Feature name'], data = feature_name)\n",
    "summary_table['Coefficients'] = np.transpose(reg_ead.coef_)\n",
    "summary_table.index = summary_table.index + 1\n",
    "summary_table.loc[0] = ['Intercept', reg_ead.intercept_]\n",
    "summary_table = summary_table.sort_index()\n",
    "p_values = reg_ead.p\n",
    "p_values = np.append(np.nan,np.array(p_values))\n",
    "summary_table['p_values'] = p_values\n",
    "summary_table.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 Model Validation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_inputs_test = ead_inputs_test[features_all]\n",
    "ead_inputs_test = ead_inputs_test.drop(features_reference_cat, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_hat_test_ead = reg_ead.predict(ead_inputs_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_targets_test_temp = ead_targets_test.copy()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [],
   "source": [
    "ead_targets_test_temp = ead_targets_test_temp.reset_index(drop = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CCF</th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>CCF</th>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.530654</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.530654</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          CCF         0\n",
       "CCF  1.000000  0.530654\n",
       "0    0.530654  1.000000"
      ]
     },
     "execution_count": 74,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the correlation\n",
    "pd.concat([ead_targets_test_temp, pd.DataFrame(y_hat_test_ead)], axis = 1).corr()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\Anaconda3\\lib\\site-packages\\seaborn\\distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:xlabel='CCF', ylabel='Density'>"
      ]
     },
     "execution_count": 75,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(ead_targets_test - y_hat_test_ead)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8648.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.736013</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.105194</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.384774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.661553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.731750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.810625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.161088</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count  8648.000000\n",
       "mean      0.736013\n",
       "std       0.105194\n",
       "min       0.384774\n",
       "25%       0.661553\n",
       "50%       0.731750\n",
       "75%       0.810625\n",
       "max       1.161088"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(y_hat_test_ead).describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>8648.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.735992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.105127</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.384774</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.661553</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.731750</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.810625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                 0\n",
       "count  8648.000000\n",
       "mean      0.735992\n",
       "std       0.105127\n",
       "min       0.384774\n",
       "25%       0.661553\n",
       "50%       0.731750\n",
       "75%       0.810625\n",
       "max       1.000000"
      ]
     },
     "execution_count": 77,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_hat_test_ead = np.where(y_hat_test_ead < 0, 0, y_hat_test_ead)\n",
    "y_hat_test_ead = np.where(y_hat_test_ead > 1, 1, y_hat_test_ead)\n",
    "pd.DataFrame(y_hat_test_ead).describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Expected Loss"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.1 Preprocess Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>id</th>\n",
       "      <th>member_id</th>\n",
       "      <th>loan_amnt</th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>funded_amnt_inv</th>\n",
       "      <th>term</th>\n",
       "      <th>int_rate</th>\n",
       "      <th>installment</th>\n",
       "      <th>...</th>\n",
       "      <th>addr_state:UT</th>\n",
       "      <th>addr_state:VA</th>\n",
       "      <th>addr_state:VT</th>\n",
       "      <th>addr_state:WA</th>\n",
       "      <th>addr_state:WI</th>\n",
       "      <th>addr_state:WV</th>\n",
       "      <th>addr_state:WY</th>\n",
       "      <th>initial_list_status:f</th>\n",
       "      <th>initial_list_status:w</th>\n",
       "      <th>good_bad</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1077501</td>\n",
       "      <td>1296599</td>\n",
       "      <td>5000</td>\n",
       "      <td>5000</td>\n",
       "      <td>4975.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>10.65</td>\n",
       "      <td>162.87</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1077430</td>\n",
       "      <td>1314167</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>15.27</td>\n",
       "      <td>59.83</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1077175</td>\n",
       "      <td>1313524</td>\n",
       "      <td>2400</td>\n",
       "      <td>2400</td>\n",
       "      <td>2400.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>15.96</td>\n",
       "      <td>84.33</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>1076863</td>\n",
       "      <td>1277178</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>13.49</td>\n",
       "      <td>339.31</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>1075358</td>\n",
       "      <td>1311748</td>\n",
       "      <td>3000</td>\n",
       "      <td>3000</td>\n",
       "      <td>3000.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>12.69</td>\n",
       "      <td>67.79</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 209 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Unnamed: 0.1       id  member_id  loan_amnt  funded_amnt  \\\n",
       "0           0             0  1077501    1296599       5000         5000   \n",
       "1           1             1  1077430    1314167       2500         2500   \n",
       "2           2             2  1077175    1313524       2400         2400   \n",
       "3           3             3  1076863    1277178      10000        10000   \n",
       "4           4             4  1075358    1311748       3000         3000   \n",
       "\n",
       "   funded_amnt_inv        term  int_rate  installment  ... addr_state:UT  \\\n",
       "0           4975.0   36 months     10.65       162.87  ...             0   \n",
       "1           2500.0   60 months     15.27        59.83  ...             0   \n",
       "2           2400.0   36 months     15.96        84.33  ...             0   \n",
       "3          10000.0   36 months     13.49       339.31  ...             0   \n",
       "4           3000.0   60 months     12.69        67.79  ...             0   \n",
       "\n",
       "  addr_state:VA addr_state:VT addr_state:WA addr_state:WI  addr_state:WV  \\\n",
       "0             0             0             0             0              0   \n",
       "1             0             0             0             0              0   \n",
       "2             0             0             0             0              0   \n",
       "3             0             0             0             0              0   \n",
       "4             0             0             0             0              0   \n",
       "\n",
       "  addr_state:WY initial_list_status:f initial_list_status:w good_bad  \n",
       "0             0                     1                     0        1  \n",
       "1             0                     1                     0        0  \n",
       "2             0                     1                     0        1  \n",
       "3             0                     1                     0        1  \n",
       "4             0                     1                     0        1  \n",
       "\n",
       "[5 rows x 209 columns]"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_preprocessed.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unnamed: 0                                                              0\n",
       "Unnamed: 0.1                                                            0\n",
       "id                                                                      0\n",
       "member_id                                                               0\n",
       "loan_amnt                                                               0\n",
       "funded_amnt                                                             0\n",
       "funded_amnt_inv                                                         0\n",
       "term                                                                    0\n",
       "int_rate                                                                0\n",
       "installment                                                             0\n",
       "grade                                                                   0\n",
       "sub_grade                                                               0\n",
       "emp_title                                                           27588\n",
       "emp_length                                                          21008\n",
       "home_ownership                                                          0\n",
       "annual_inc                                                              0\n",
       "verification_status                                                     0\n",
       "issue_d                                                                 0\n",
       "loan_status                                                             0\n",
       "pymnt_plan                                                              0\n",
       "url                                                                     0\n",
       "desc                                                               340302\n",
       "purpose                                                                 0\n",
       "title                                                                  20\n",
       "zip_code                                                                0\n",
       "addr_state                                                              0\n",
       "dti                                                                     0\n",
       "delinq_2yrs                                                             0\n",
       "earliest_cr_line                                                       29\n",
       "inq_last_6mths                                                          0\n",
       "mths_since_last_delinq                                             250351\n",
       "mths_since_last_record                                             403647\n",
       "open_acc                                                                0\n",
       "pub_rec                                                                 0\n",
       "revol_bal                                                               0\n",
       "revol_util                                                            340\n",
       "total_acc                                                               0\n",
       "initial_list_status                                                     0\n",
       "out_prncp                                                               0\n",
       "out_prncp_inv                                                           0\n",
       "total_pymnt                                                             0\n",
       "total_pymnt_inv                                                         0\n",
       "total_rec_prncp                                                         0\n",
       "total_rec_int                                                           0\n",
       "total_rec_late_fee                                                      0\n",
       "recoveries                                                              0\n",
       "collection_recovery_fee                                                 0\n",
       "last_pymnt_d                                                          376\n",
       "last_pymnt_amnt                                                         0\n",
       "next_pymnt_d                                                       227214\n",
       "last_credit_pull_d                                                     42\n",
       "collections_12_mths_ex_med                                            145\n",
       "mths_since_last_major_derog                                        367311\n",
       "policy_code                                                             0\n",
       "application_type                                                        0\n",
       "annual_inc_joint                                                   466285\n",
       "dti_joint                                                          466285\n",
       "verification_status_joint                                          466285\n",
       "acc_now_delinq                                                          0\n",
       "tot_coll_amt                                                        70276\n",
       "tot_cur_bal                                                         70276\n",
       "open_acc_6m                                                        466285\n",
       "open_il_6m                                                         466285\n",
       "open_il_12m                                                        466285\n",
       "open_il_24m                                                        466285\n",
       "mths_since_rcnt_il                                                 466285\n",
       "total_bal_il                                                       466285\n",
       "il_util                                                            466285\n",
       "open_rv_12m                                                        466285\n",
       "open_rv_24m                                                        466285\n",
       "max_bal_bc                                                         466285\n",
       "all_util                                                           466285\n",
       "total_rev_hi_lim                                                        0\n",
       "inq_fi                                                             466285\n",
       "total_cu_tl                                                        466285\n",
       "inq_last_12m                                                       466285\n",
       "emp_length_int                                                          0\n",
       "earliest_cr_line_date                                                  29\n",
       "mths_since_earliest_cr_line                                             0\n",
       "term_int                                                                0\n",
       "issue_d_date                                                            0\n",
       "mths_since_issue_d                                                      0\n",
       "grade:A                                                                 0\n",
       "grade:B                                                                 0\n",
       "grade:C                                                                 0\n",
       "grade:D                                                                 0\n",
       "grade:E                                                                 0\n",
       "grade:F                                                                 0\n",
       "grade:G                                                                 0\n",
       "sub_grade:A1                                                            0\n",
       "sub_grade:A2                                                            0\n",
       "sub_grade:A3                                                            0\n",
       "sub_grade:A4                                                            0\n",
       "sub_grade:A5                                                            0\n",
       "sub_grade:B1                                                            0\n",
       "sub_grade:B2                                                            0\n",
       "sub_grade:B3                                                            0\n",
       "sub_grade:B4                                                            0\n",
       "sub_grade:B5                                                            0\n",
       "sub_grade:C1                                                            0\n",
       "sub_grade:C2                                                            0\n",
       "sub_grade:C3                                                            0\n",
       "sub_grade:C4                                                            0\n",
       "sub_grade:C5                                                            0\n",
       "sub_grade:D1                                                            0\n",
       "sub_grade:D2                                                            0\n",
       "sub_grade:D3                                                            0\n",
       "sub_grade:D4                                                            0\n",
       "sub_grade:D5                                                            0\n",
       "sub_grade:E1                                                            0\n",
       "sub_grade:E2                                                            0\n",
       "sub_grade:E3                                                            0\n",
       "sub_grade:E4                                                            0\n",
       "sub_grade:E5                                                            0\n",
       "sub_grade:F1                                                            0\n",
       "sub_grade:F2                                                            0\n",
       "sub_grade:F3                                                            0\n",
       "sub_grade:F4                                                            0\n",
       "sub_grade:F5                                                            0\n",
       "sub_grade:G1                                                            0\n",
       "sub_grade:G2                                                            0\n",
       "sub_grade:G3                                                            0\n",
       "sub_grade:G4                                                            0\n",
       "sub_grade:G5                                                            0\n",
       "home_ownership:ANY                                                      0\n",
       "home_ownership:MORTGAGE                                                 0\n",
       "home_ownership:NONE                                                     0\n",
       "home_ownership:OTHER                                                    0\n",
       "home_ownership:OWN                                                      0\n",
       "home_ownership:RENT                                                     0\n",
       "verification_status:Not Verified                                        0\n",
       "verification_status:Source Verified                                     0\n",
       "verification_status:Verified                                            0\n",
       "loan_status:Charged Off                                                 0\n",
       "loan_status:Current                                                     0\n",
       "loan_status:Default                                                     0\n",
       "loan_status:Does not meet the credit policy. Status:Charged Off         0\n",
       "loan_status:Does not meet the credit policy. Status:Fully Paid          0\n",
       "loan_status:Fully Paid                                                  0\n",
       "loan_status:In Grace Period                                             0\n",
       "loan_status:Late (16-30 days)                                           0\n",
       "loan_status:Late (31-120 days)                                          0\n",
       "purpose:car                                                             0\n",
       "purpose:credit_card                                                     0\n",
       "purpose:debt_consolidation                                              0\n",
       "purpose:educational                                                     0\n",
       "purpose:home_improvement                                                0\n",
       "purpose:house                                                           0\n",
       "purpose:major_purchase                                                  0\n",
       "purpose:medical                                                         0\n",
       "purpose:moving                                                          0\n",
       "purpose:other                                                           0\n",
       "purpose:renewable_energy                                                0\n",
       "purpose:small_business                                                  0\n",
       "purpose:vacation                                                        0\n",
       "purpose:wedding                                                         0\n",
       "addr_state:AK                                                           0\n",
       "addr_state:AL                                                           0\n",
       "addr_state:AR                                                           0\n",
       "addr_state:AZ                                                           0\n",
       "addr_state:CA                                                           0\n",
       "addr_state:CO                                                           0\n",
       "addr_state:CT                                                           0\n",
       "addr_state:DC                                                           0\n",
       "addr_state:DE                                                           0\n",
       "addr_state:FL                                                           0\n",
       "addr_state:GA                                                           0\n",
       "addr_state:HI                                                           0\n",
       "addr_state:IA                                                           0\n",
       "addr_state:ID                                                           0\n",
       "addr_state:IL                                                           0\n",
       "addr_state:IN                                                           0\n",
       "addr_state:KS                                                           0\n",
       "addr_state:KY                                                           0\n",
       "addr_state:LA                                                           0\n",
       "addr_state:MA                                                           0\n",
       "addr_state:MD                                                           0\n",
       "addr_state:ME                                                           0\n",
       "addr_state:MI                                                           0\n",
       "addr_state:MN                                                           0\n",
       "addr_state:MO                                                           0\n",
       "addr_state:MS                                                           0\n",
       "addr_state:MT                                                           0\n",
       "addr_state:NC                                                           0\n",
       "addr_state:NE                                                           0\n",
       "addr_state:NH                                                           0\n",
       "addr_state:NJ                                                           0\n",
       "addr_state:NM                                                           0\n",
       "addr_state:NV                                                           0\n",
       "addr_state:NY                                                           0\n",
       "addr_state:OH                                                           0\n",
       "addr_state:OK                                                           0\n",
       "addr_state:OR                                                           0\n",
       "addr_state:PA                                                           0\n",
       "addr_state:RI                                                           0\n",
       "addr_state:SC                                                           0\n",
       "addr_state:SD                                                           0\n",
       "addr_state:TN                                                           0\n",
       "addr_state:TX                                                           0\n",
       "addr_state:UT                                                           0\n",
       "addr_state:VA                                                           0\n",
       "addr_state:VT                                                           0\n",
       "addr_state:WA                                                           0\n",
       "addr_state:WI                                                           0\n",
       "addr_state:WV                                                           0\n",
       "addr_state:WY                                                           0\n",
       "initial_list_status:f                                                   0\n",
       "initial_list_status:w                                                   0\n",
       "good_bad                                                                0\n",
       "dtype: int64"
      ]
     },
     "execution_count": 79,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_preprocessed.isnull().sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fill the missing values\n",
    "loan_data_preprocessed['mths_since_last_delinq'].fillna(0, inplace = True)\n",
    "loan_data_preprocessed['mths_since_last_record'].fillna(0, inplace = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep the needed variables\n",
    "loan_data_preprocessed_lgd_ead = loan_data_preprocessed[features_all]\n",
    "loan_data_preprocessed_lgd_ead = loan_data_preprocessed_lgd_ead.drop(features_reference_cat, axis = 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.2 LGD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Apply LGD stage 1 - Logistic regression model\n",
    "loan_data_preprocessed['recovery_rate_st_1'] = \\\n",
    "reg_lgd_st_1.model.predict(loan_data_preprocessed_lgd_ead)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Apply LGD stage 2 - Linear regression model\n",
    "loan_data_preprocessed['recovery_rate_st_2'] = \\\n",
    "reg_lgd_st_2.predict(loan_data_preprocessed_lgd_ead)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Multiply the result the calculate the recovery rate\n",
    "loan_data_preprocessed['recovery_rate'] = \\\n",
    "loan_data_preprocessed['recovery_rate_st_1'] * \\\n",
    "loan_data_preprocessed['recovery_rate_st_2']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Make sure all values between 0 and 1\n",
    "loan_data_preprocessed['recovery_rate'] = np.where(loan_data_preprocessed['recovery_rate'] < 0, 0, loan_data_preprocessed['recovery_rate'])\n",
    "loan_data_preprocessed['recovery_rate'] = np.where(loan_data_preprocessed['recovery_rate'] > 1, 1, loan_data_preprocessed['recovery_rate'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    466285.000000\n",
       "mean          0.920118\n",
       "std           0.057379\n",
       "min           0.371789\n",
       "25%           0.873563\n",
       "50%           0.899121\n",
       "75%           1.000000\n",
       "max           1.000000\n",
       "Name: LGD, dtype: float64"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Calculate the LGD\n",
    "loan_data_preprocessed['LGD'] = 1 - loan_data_preprocessed['recovery_rate']\n",
    "loan_data_preprocessed['LGD'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.3 EAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_data_preprocessed['CCF'] = reg_ead.predict(loan_data_preprocessed_lgd_ead)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_data_preprocessed['CCF'] = np.where(loan_data_preprocessed['CCF'] < 0, 0, loan_data_preprocessed['CCF'])\n",
    "loan_data_preprocessed['CCF'] = np.where(loan_data_preprocessed['CCF'] > 1, 1, loan_data_preprocessed['CCF'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    466285.000000\n",
       "mean      10814.846760\n",
       "std        6935.184562\n",
       "min         190.347372\n",
       "25%        5495.101413\n",
       "50%        9208.479591\n",
       "75%       14692.844549\n",
       "max       35000.000000\n",
       "Name: EAD, dtype: float64"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_preprocessed['EAD'] = \\\n",
    "loan_data_preprocessed['CCF'] * loan_data_preprocessed_lgd_ead['funded_amnt']\n",
    "# Calculate estimated EAD. \n",
    "# Estimated EAD equals estimated CCF multiplied by funded amount.\n",
    "loan_data_preprocessed['EAD'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>id</th>\n",
       "      <th>member_id</th>\n",
       "      <th>loan_amnt</th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>funded_amnt_inv</th>\n",
       "      <th>term</th>\n",
       "      <th>int_rate</th>\n",
       "      <th>installment</th>\n",
       "      <th>...</th>\n",
       "      <th>addr_state:WY</th>\n",
       "      <th>initial_list_status:f</th>\n",
       "      <th>initial_list_status:w</th>\n",
       "      <th>good_bad</th>\n",
       "      <th>recovery_rate_st_1</th>\n",
       "      <th>recovery_rate_st_2</th>\n",
       "      <th>recovery_rate</th>\n",
       "      <th>LGD</th>\n",
       "      <th>CCF</th>\n",
       "      <th>EAD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1077501</td>\n",
       "      <td>1296599</td>\n",
       "      <td>5000</td>\n",
       "      <td>5000</td>\n",
       "      <td>4975.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>10.65</td>\n",
       "      <td>162.87</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.086271</td>\n",
       "      <td>0.086271</td>\n",
       "      <td>0.913729</td>\n",
       "      <td>0.589922</td>\n",
       "      <td>2949.608449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1077430</td>\n",
       "      <td>1314167</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>15.27</td>\n",
       "      <td>59.83</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0.084518</td>\n",
       "      <td>0.084518</td>\n",
       "      <td>0.915482</td>\n",
       "      <td>0.777773</td>\n",
       "      <td>1944.433378</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1077175</td>\n",
       "      <td>1313524</td>\n",
       "      <td>2400</td>\n",
       "      <td>2400</td>\n",
       "      <td>2400.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>15.96</td>\n",
       "      <td>84.33</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.080516</td>\n",
       "      <td>0.080516</td>\n",
       "      <td>0.919484</td>\n",
       "      <td>0.658306</td>\n",
       "      <td>1579.934302</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>1076863</td>\n",
       "      <td>1277178</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>13.49</td>\n",
       "      <td>339.31</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.095076</td>\n",
       "      <td>0.095076</td>\n",
       "      <td>0.904924</td>\n",
       "      <td>0.660656</td>\n",
       "      <td>6606.559612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>1075358</td>\n",
       "      <td>1311748</td>\n",
       "      <td>3000</td>\n",
       "      <td>3000</td>\n",
       "      <td>3000.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>12.69</td>\n",
       "      <td>67.79</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>0.088547</td>\n",
       "      <td>0.088547</td>\n",
       "      <td>0.911453</td>\n",
       "      <td>0.708211</td>\n",
       "      <td>2124.631667</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 215 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Unnamed: 0.1       id  member_id  loan_amnt  funded_amnt  \\\n",
       "0           0             0  1077501    1296599       5000         5000   \n",
       "1           1             1  1077430    1314167       2500         2500   \n",
       "2           2             2  1077175    1313524       2400         2400   \n",
       "3           3             3  1076863    1277178      10000        10000   \n",
       "4           4             4  1075358    1311748       3000         3000   \n",
       "\n",
       "   funded_amnt_inv        term  int_rate  installment  ... addr_state:WY  \\\n",
       "0           4975.0   36 months     10.65       162.87  ...             0   \n",
       "1           2500.0   60 months     15.27        59.83  ...             0   \n",
       "2           2400.0   36 months     15.96        84.33  ...             0   \n",
       "3          10000.0   36 months     13.49       339.31  ...             0   \n",
       "4           3000.0   60 months     12.69        67.79  ...             0   \n",
       "\n",
       "  initial_list_status:f initial_list_status:w good_bad recovery_rate_st_1  \\\n",
       "0                     1                     0        1                  1   \n",
       "1                     1                     0        0                  1   \n",
       "2                     1                     0        1                  1   \n",
       "3                     1                     0        1                  1   \n",
       "4                     1                     0        1                  1   \n",
       "\n",
       "   recovery_rate_st_2 recovery_rate       LGD       CCF          EAD  \n",
       "0            0.086271      0.086271  0.913729  0.589922  2949.608449  \n",
       "1            0.084518      0.084518  0.915482  0.777773  1944.433378  \n",
       "2            0.080516      0.080516  0.919484  0.658306  1579.934302  \n",
       "3            0.095076      0.095076  0.904924  0.660656  6606.559612  \n",
       "4            0.088547      0.088547  0.911453  0.708211  2124.631667  \n",
       "\n",
       "[5 rows x 215 columns]"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_preprocessed.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.4 PD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_data_inputs_train = pd.read_csv('loan_data_inputs_train.csv')\n",
    "loan_data_inputs_test = pd.read_csv('loan_data_inputs_test.csv')\n",
    "# Import data to apply the PD model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <td>10000.0</td>\n",
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       "      <td>14.33</td>\n",
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       "      <td>6556909</td>\n",
       "      <td>20425</td>\n",
       "      <td>20425</td>\n",
       "      <td>20425.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>8.90</td>\n",
       "      <td>648.56</td>\n",
       "      <td>...</td>\n",
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       "      <td>0</td>\n",
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       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>412305</td>\n",
       "      <td>412305</td>\n",
       "      <td>13827698</td>\n",
       "      <td>15890016</td>\n",
       "      <td>17200</td>\n",
       "      <td>17200</td>\n",
       "      <td>17200.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>16.59</td>\n",
       "      <td>609.73</td>\n",
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       "      <td>36159</td>\n",
       "      <td>36159</td>\n",
       "      <td>422455</td>\n",
       "      <td>496525</td>\n",
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       "      <td>8400</td>\n",
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       "      <td>36 months</td>\n",
       "      <td>12.84</td>\n",
       "      <td>282.40</td>\n",
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      ],
      "text/plain": [
       "   Unnamed: 0  Unnamed: 0.1        id  member_id  loan_amnt  funded_amnt  \\\n",
       "0      427211        427211  12796369   14818505      24000        24000   \n",
       "1      206088        206088   1439740    1691948      10000        10000   \n",
       "2      136020        136020   5214749    6556909      20425        20425   \n",
       "3      412305        412305  13827698   15890016      17200        17200   \n",
       "4       36159         36159    422455     496525       8400         8400   \n",
       "\n",
       "   funded_amnt_inv        term  int_rate  installment  ... dti:21.7-22.4  \\\n",
       "0          24000.0   36 months      8.90       762.08  ...             1   \n",
       "1          10000.0   36 months     14.33       343.39  ...             0   \n",
       "2          20425.0   36 months      8.90       648.56  ...             0   \n",
       "3          17200.0   36 months     16.59       609.73  ...             0   \n",
       "4           7450.0   36 months     12.84       282.40  ...             0   \n",
       "\n",
       "  dti:22.4-35 dti:>35 mths_since_last_record:Missing  \\\n",
       "0           0       0                              1   \n",
       "1           0       0                              1   \n",
       "2           0       0                              1   \n",
       "3           0       0                              1   \n",
       "4           1       0                              1   \n",
       "\n",
       "  mths_since_last_record:0-2  mths_since_last_record:3-20  \\\n",
       "0                          0                            0   \n",
       "1                          0                            0   \n",
       "2                          0                            0   \n",
       "3                          0                            0   \n",
       "4                          0                            0   \n",
       "\n",
       "  mths_since_last_record:21-31 mths_since_last_record:32-80  \\\n",
       "0                            0                            0   \n",
       "1                            0                            0   \n",
       "2                            0                            0   \n",
       "3                            0                            0   \n",
       "4                            0                            0   \n",
       "\n",
       "  mths_since_last_record:81-86 mths_since_last_record:>86  \n",
       "0                            0                          0  \n",
       "1                            0                          0  \n",
       "2                            0                          0  \n",
       "3                            0                          0  \n",
       "4                            0                          0  \n",
       "\n",
       "[5 rows x 325 columns]"
      ]
     },
     "execution_count": 92,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_inputs_pd = \\\n",
    "pd.concat([loan_data_inputs_train, loan_data_inputs_test], axis = 0)\n",
    "# Concatenate the two dataframes along the rows.\n",
    "loan_data_inputs_pd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>Unnamed: 0.1</th>\n",
       "      <th>id</th>\n",
       "      <th>member_id</th>\n",
       "      <th>loan_amnt</th>\n",
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       "      <th>...</th>\n",
       "      <th>dti:21.7-22.4</th>\n",
       "      <th>dti:22.4-35</th>\n",
       "      <th>dti:&gt;35</th>\n",
       "      <th>mths_since_last_record:Missing</th>\n",
       "      <th>mths_since_last_record:0-2</th>\n",
       "      <th>mths_since_last_record:3-20</th>\n",
       "      <th>mths_since_last_record:21-31</th>\n",
       "      <th>mths_since_last_record:32-80</th>\n",
       "      <th>mths_since_last_record:81-86</th>\n",
       "      <th>mths_since_last_record:&gt;86</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>427211</th>\n",
       "      <td>427211</td>\n",
       "      <td>12796369</td>\n",
       "      <td>14818505</td>\n",
       "      <td>24000</td>\n",
       "      <td>24000</td>\n",
       "      <td>24000.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>8.90</td>\n",
       "      <td>762.08</td>\n",
       "      <td>A</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>206088</th>\n",
       "      <td>206088</td>\n",
       "      <td>1439740</td>\n",
       "      <td>1691948</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>14.33</td>\n",
       "      <td>343.39</td>\n",
       "      <td>C</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136020</th>\n",
       "      <td>136020</td>\n",
       "      <td>5214749</td>\n",
       "      <td>6556909</td>\n",
       "      <td>20425</td>\n",
       "      <td>20425</td>\n",
       "      <td>20425.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>8.90</td>\n",
       "      <td>648.56</td>\n",
       "      <td>A</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>412305</th>\n",
       "      <td>412305</td>\n",
       "      <td>13827698</td>\n",
       "      <td>15890016</td>\n",
       "      <td>17200</td>\n",
       "      <td>17200</td>\n",
       "      <td>17200.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>16.59</td>\n",
       "      <td>609.73</td>\n",
       "      <td>D</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36159</th>\n",
       "      <td>36159</td>\n",
       "      <td>422455</td>\n",
       "      <td>496525</td>\n",
       "      <td>8400</td>\n",
       "      <td>8400</td>\n",
       "      <td>7450.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>12.84</td>\n",
       "      <td>282.40</td>\n",
       "      <td>C</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 324 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Unnamed: 0.1        id  member_id  loan_amnt  funded_amnt  \\\n",
       "Unnamed: 0                                                              \n",
       "427211            427211  12796369   14818505      24000        24000   \n",
       "206088            206088   1439740    1691948      10000        10000   \n",
       "136020            136020   5214749    6556909      20425        20425   \n",
       "412305            412305  13827698   15890016      17200        17200   \n",
       "36159              36159    422455     496525       8400         8400   \n",
       "\n",
       "            funded_amnt_inv        term  int_rate  installment grade  ...  \\\n",
       "Unnamed: 0                                                            ...   \n",
       "427211              24000.0   36 months      8.90       762.08     A  ...   \n",
       "206088              10000.0   36 months     14.33       343.39     C  ...   \n",
       "136020              20425.0   36 months      8.90       648.56     A  ...   \n",
       "412305              17200.0   36 months     16.59       609.73     D  ...   \n",
       "36159                7450.0   36 months     12.84       282.40     C  ...   \n",
       "\n",
       "           dti:21.7-22.4 dti:22.4-35 dti:>35 mths_since_last_record:Missing  \\\n",
       "Unnamed: 0                                                                    \n",
       "427211                 1           0       0                              1   \n",
       "206088                 0           0       0                              1   \n",
       "136020                 0           0       0                              1   \n",
       "412305                 0           0       0                              1   \n",
       "36159                  0           1       0                              1   \n",
       "\n",
       "            mths_since_last_record:0-2 mths_since_last_record:3-20  \\\n",
       "Unnamed: 0                                                           \n",
       "427211                               0                           0   \n",
       "206088                               0                           0   \n",
       "136020                               0                           0   \n",
       "412305                               0                           0   \n",
       "36159                                0                           0   \n",
       "\n",
       "           mths_since_last_record:21-31 mths_since_last_record:32-80  \\\n",
       "Unnamed: 0                                                             \n",
       "427211                                0                            0   \n",
       "206088                                0                            0   \n",
       "136020                                0                            0   \n",
       "412305                                0                            0   \n",
       "36159                                 0                            0   \n",
       "\n",
       "           mths_since_last_record:81-86 mths_since_last_record:>86  \n",
       "Unnamed: 0                                                          \n",
       "427211                                0                          0  \n",
       "206088                                0                          0  \n",
       "136020                                0                          0  \n",
       "412305                                0                          0  \n",
       "36159                                 0                          0  \n",
       "\n",
       "[5 rows x 324 columns]"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_inputs_pd = loan_data_inputs_pd.set_index('Unnamed: 0')\n",
    "loan_data_inputs_pd.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "features_all_pd = ['grade:A',\n",
    "'grade:B',\n",
    "'grade:C',\n",
    "'grade:D',\n",
    "'grade:E',\n",
    "'grade:F',\n",
    "'grade:G',\n",
    "'home_ownership:RENT_OTHER_NONE_ANY',\n",
    "'home_ownership:OWN',\n",
    "'home_ownership:MORTGAGE',\n",
    "'addr_state:ND_NE_IA_NV_FL_HI_AL',\n",
    "'addr_state:NM_VA',\n",
    "'addr_state:NY',\n",
    "'addr_state:OK_TN_MO_LA_MD_NC',\n",
    "'addr_state:CA',\n",
    "'addr_state:UT_KY_AZ_NJ',\n",
    "'addr_state:AR_MI_PA_OH_MN',\n",
    "'addr_state:RI_MA_DE_SD_IN',\n",
    "'addr_state:GA_WA_OR',\n",
    "'addr_state:WI_MT',\n",
    "'addr_state:TX',\n",
    "'addr_state:IL_CT',\n",
    "'addr_state:KS_SC_CO_VT_AK_MS',\n",
    "'addr_state:WV_NH_WY_DC_ME_ID',\n",
    "'verification_status:Not Verified',\n",
    "'verification_status:Source Verified',\n",
    "'verification_status:Verified',\n",
    "'purpose:educ__sm_b__wedd__ren_en__mov__house',\n",
    "'purpose:credit_card',\n",
    "'purpose:debt_consolidation',\n",
    "'purpose:oth__med__vacation',\n",
    "'purpose:major_purch__car__home_impr',\n",
    "'initial_list_status:f',\n",
    "'initial_list_status:w',\n",
    "'term:36',\n",
    "'term:60',\n",
    "'emp_length:0',\n",
    "'emp_length:1',\n",
    "'emp_length:2-4',\n",
    "'emp_length:5-6',\n",
    "'emp_length:7-9',\n",
    "'emp_length:10',\n",
    "'mths_since_issue_d:<38',\n",
    "'mths_since_issue_d:38-39',\n",
    "'mths_since_issue_d:40-41',\n",
    "'mths_since_issue_d:42-48',\n",
    "'mths_since_issue_d:49-52',\n",
    "'mths_since_issue_d:53-64',\n",
    "'mths_since_issue_d:65-84',\n",
    "'mths_since_issue_d:>84',\n",
    "'int_rate:<9.548',\n",
    "'int_rate:9.548-12.025',\n",
    "'int_rate:12.025-15.74',\n",
    "'int_rate:15.74-20.281',\n",
    "'int_rate:>20.281',\n",
    "'mths_since_earliest_cr_line:<140',\n",
    "'mths_since_earliest_cr_line:141-164',\n",
    "'mths_since_earliest_cr_line:165-247',\n",
    "'mths_since_earliest_cr_line:248-270',\n",
    "'mths_since_earliest_cr_line:271-352',\n",
    "'mths_since_earliest_cr_line:>352',\n",
    "'inq_last_6mths:0',\n",
    "'inq_last_6mths:1-2',\n",
    "'inq_last_6mths:3-6',\n",
    "'inq_last_6mths:>6',\n",
    "'acc_now_delinq:0',\n",
    "'acc_now_delinq:>=1',\n",
    "'annual_inc:<20K',\n",
    "'annual_inc:20K-30K',\n",
    "'annual_inc:30K-40K',\n",
    "'annual_inc:40K-50K',\n",
    "'annual_inc:50K-60K',\n",
    "'annual_inc:60K-70K',\n",
    "'annual_inc:70K-80K',\n",
    "'annual_inc:80K-90K',\n",
    "'annual_inc:90K-100K',\n",
    "'annual_inc:100K-120K',\n",
    "'annual_inc:120K-140K',\n",
    "'annual_inc:>140K',\n",
    "'dti:<=1.4',\n",
    "'dti:1.4-3.5',\n",
    "'dti:3.5-7.7',\n",
    "'dti:7.7-10.5',\n",
    "'dti:10.5-16.1',\n",
    "'dti:16.1-20.3',\n",
    "'dti:20.3-21.7',\n",
    "'dti:21.7-22.4',\n",
    "'dti:22.4-35',\n",
    "'dti:>35',\n",
    "'mths_since_last_delinq:Missing',\n",
    "'mths_since_last_delinq:0-3',\n",
    "'mths_since_last_delinq:4-30',\n",
    "'mths_since_last_delinq:31-56',\n",
    "'mths_since_last_delinq:>=57',\n",
    "'mths_since_last_record:Missing',\n",
    "'mths_since_last_record:0-2',\n",
    "'mths_since_last_record:3-20',\n",
    "'mths_since_last_record:21-31',\n",
    "'mths_since_last_record:32-80',\n",
    "'mths_since_last_record:81-86',\n",
    "'mths_since_last_record:>86']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [],
   "source": [
    "ref_categories_pd = ['grade:G',\n",
    "'home_ownership:RENT_OTHER_NONE_ANY',\n",
    "'addr_state:ND_NE_IA_NV_FL_HI_AL',\n",
    "'verification_status:Verified',\n",
    "'purpose:educ__sm_b__wedd__ren_en__mov__house',\n",
    "'initial_list_status:f',\n",
    "'term:60',\n",
    "'emp_length:0',\n",
    "'mths_since_issue_d:>84',\n",
    "'int_rate:>20.281',\n",
    "'mths_since_earliest_cr_line:<140',\n",
    "'inq_last_6mths:>6',\n",
    "'acc_now_delinq:0',\n",
    "'annual_inc:<20K',\n",
    "'dti:>35',\n",
    "'mths_since_last_delinq:0-3',\n",
    "'mths_since_last_record:0-2']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Keep the needed variables\n",
    "loan_data_inputs_pd_temp = loan_data_inputs_pd[features_all_pd]\n",
    "loan_data_inputs_pd_temp = loan_data_inputs_pd_temp.drop(ref_categories_pd, axis = 1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(466285, 84)"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_inputs_pd_temp.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import PD model\n",
    "import pickle\n",
    "reg_pd = pickle.load(open('pd_model.sav', 'rb'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.02958552, 0.0921482 , 0.03735908, ..., 0.02678659, 0.04020859,\n",
       "       0.04763349])"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Only get the probability of defaults\n",
    "pd_value = reg_pd.model.predict_proba(loan_data_inputs_pd_temp)[: ][: , 0]\n",
    "pd_value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Unnamed: 0\n",
       "427211    0.029586\n",
       "206088    0.092148\n",
       "136020    0.037359\n",
       "412305    0.204328\n",
       "36159     0.200847\n",
       "Name: PD, dtype: float64"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_inputs_pd['PD'] = pd_value\n",
    "loan_data_inputs_pd['PD'].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    466285.000000\n",
       "mean          0.109307\n",
       "std           0.070917\n",
       "min           0.007314\n",
       "25%           0.056064\n",
       "50%           0.093492\n",
       "75%           0.146558\n",
       "max           0.635818\n",
       "Name: PD, dtype: float64"
      ]
     },
     "execution_count": 101,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_inputs_pd['PD'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>Unnamed: 0.1</th>\n",
       "      <th>id</th>\n",
       "      <th>member_id</th>\n",
       "      <th>loan_amnt</th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>funded_amnt_inv</th>\n",
       "      <th>term</th>\n",
       "      <th>int_rate</th>\n",
       "      <th>installment</th>\n",
       "      <th>...</th>\n",
       "      <th>dti:22.4-35</th>\n",
       "      <th>dti:&gt;35</th>\n",
       "      <th>mths_since_last_record:Missing</th>\n",
       "      <th>mths_since_last_record:0-2</th>\n",
       "      <th>mths_since_last_record:3-20</th>\n",
       "      <th>mths_since_last_record:21-31</th>\n",
       "      <th>mths_since_last_record:32-80</th>\n",
       "      <th>mths_since_last_record:81-86</th>\n",
       "      <th>mths_since_last_record:&gt;86</th>\n",
       "      <th>PD</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1077501</td>\n",
       "      <td>1296599</td>\n",
       "      <td>5000</td>\n",
       "      <td>5000</td>\n",
       "      <td>4975.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>10.65</td>\n",
       "      <td>162.87</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.164761</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>1077430</td>\n",
       "      <td>1314167</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500</td>\n",
       "      <td>2500.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>15.27</td>\n",
       "      <td>59.83</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.282340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>1077175</td>\n",
       "      <td>1313524</td>\n",
       "      <td>2400</td>\n",
       "      <td>2400</td>\n",
       "      <td>2400.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>15.96</td>\n",
       "      <td>84.33</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.229758</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>3</td>\n",
       "      <td>3</td>\n",
       "      <td>1076863</td>\n",
       "      <td>1277178</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000</td>\n",
       "      <td>10000.0</td>\n",
       "      <td>36 months</td>\n",
       "      <td>13.49</td>\n",
       "      <td>339.31</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.208892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>1075358</td>\n",
       "      <td>1311748</td>\n",
       "      <td>3000</td>\n",
       "      <td>3000</td>\n",
       "      <td>3000.0</td>\n",
       "      <td>60 months</td>\n",
       "      <td>12.69</td>\n",
       "      <td>67.79</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0.129556</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 540 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  Unnamed: 0.1       id  member_id  loan_amnt  funded_amnt  \\\n",
       "0           0             0  1077501    1296599       5000         5000   \n",
       "1           1             1  1077430    1314167       2500         2500   \n",
       "2           2             2  1077175    1313524       2400         2400   \n",
       "3           3             3  1076863    1277178      10000        10000   \n",
       "4           4             4  1075358    1311748       3000         3000   \n",
       "\n",
       "   funded_amnt_inv        term  int_rate  installment  ... dti:22.4-35  \\\n",
       "0           4975.0   36 months     10.65       162.87  ...           1   \n",
       "1           2500.0   60 months     15.27        59.83  ...           0   \n",
       "2           2400.0   36 months     15.96        84.33  ...           0   \n",
       "3          10000.0   36 months     13.49       339.31  ...           0   \n",
       "4           3000.0   60 months     12.69        67.79  ...           0   \n",
       "\n",
       "  dti:>35 mths_since_last_record:Missing mths_since_last_record:0-2  \\\n",
       "0       0                              1                          0   \n",
       "1       0                              1                          0   \n",
       "2       0                              1                          0   \n",
       "3       0                              1                          0   \n",
       "4       0                              1                          0   \n",
       "\n",
       "  mths_since_last_record:3-20  mths_since_last_record:21-31  \\\n",
       "0                           0                             0   \n",
       "1                           0                             0   \n",
       "2                           0                             0   \n",
       "3                           0                             0   \n",
       "4                           0                             0   \n",
       "\n",
       "  mths_since_last_record:32-80 mths_since_last_record:81-86  \\\n",
       "0                            0                            0   \n",
       "1                            0                            0   \n",
       "2                            0                            0   \n",
       "3                            0                            0   \n",
       "4                            0                            0   \n",
       "\n",
       "  mths_since_last_record:>86        PD  \n",
       "0                          0  0.164761  \n",
       "1                          0  0.282340  \n",
       "2                          0  0.229758  \n",
       "3                          0  0.208892  \n",
       "4                          0  0.129556  \n",
       "\n",
       "[5 rows x 540 columns]"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Concate PD with LGD and EAD\n",
    "loan_data_preprocessed_new = \\\n",
    "pd.concat([loan_data_preprocessed, loan_data_inputs_pd], axis = 1)\n",
    "loan_data_preprocessed_new.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 6.5 EL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_data_preprocessed_new['EL'] = loan_data_preprocessed_new['PD'] * \\\n",
    "loan_data_preprocessed_new['LGD'] * loan_data_preprocessed_new['EAD']\n",
    "# Calculate Expected Loss. EL = PD * LGD * EAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "loan_data_EL = loan_data_preprocessed_new[['funded_amnt', 'PD', 'LGD', 'EAD', 'EL']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>PD</th>\n",
       "      <th>LGD</th>\n",
       "      <th>EAD</th>\n",
       "      <th>EL</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5000</td>\n",
       "      <td>5000</td>\n",
       "      <td>0.164761</td>\n",
       "      <td>0.913729</td>\n",
       "      <td>2949.608449</td>\n",
       "      <td>444.053181</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2500</td>\n",
       "      <td>2500</td>\n",
       "      <td>0.282340</td>\n",
       "      <td>0.915482</td>\n",
       "      <td>1944.433378</td>\n",
       "      <td>502.592155</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2400</td>\n",
       "      <td>2400</td>\n",
       "      <td>0.229758</td>\n",
       "      <td>0.919484</td>\n",
       "      <td>1579.934302</td>\n",
       "      <td>333.775277</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>10000</td>\n",
       "      <td>10000</td>\n",
       "      <td>0.208892</td>\n",
       "      <td>0.904924</td>\n",
       "      <td>6606.559612</td>\n",
       "      <td>1248.848487</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3000</td>\n",
       "      <td>3000</td>\n",
       "      <td>0.129556</td>\n",
       "      <td>0.911453</td>\n",
       "      <td>2124.631667</td>\n",
       "      <td>250.884853</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   funded_amnt  funded_amnt        PD       LGD          EAD           EL\n",
       "0         5000         5000  0.164761  0.913729  2949.608449   444.053181\n",
       "1         2500         2500  0.282340  0.915482  1944.433378   502.592155\n",
       "2         2400         2400  0.229758  0.919484  1579.934302   333.775277\n",
       "3        10000        10000  0.208892  0.904924  6606.559612  1248.848487\n",
       "4         3000         3000  0.129556  0.911453  2124.631667   250.884853"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_EL.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>funded_amnt</th>\n",
       "      <th>funded_amnt</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>466285.000000</td>\n",
       "      <td>466285.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>14291.801044</td>\n",
       "      <td>14291.801044</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>8274.371300</td>\n",
       "      <td>8274.371300</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>500.000000</td>\n",
       "      <td>500.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>8000.000000</td>\n",
       "      <td>8000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>12000.000000</td>\n",
       "      <td>12000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>20000.000000</td>\n",
       "      <td>20000.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>35000.000000</td>\n",
       "      <td>35000.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         funded_amnt    funded_amnt\n",
       "count  466285.000000  466285.000000\n",
       "mean    14291.801044   14291.801044\n",
       "std      8274.371300    8274.371300\n",
       "min       500.000000     500.000000\n",
       "25%      8000.000000    8000.000000\n",
       "50%     12000.000000   12000.000000\n",
       "75%     20000.000000   20000.000000\n",
       "max     35000.000000   35000.000000"
      ]
     },
     "execution_count": 106,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "loan_data_EL['funded_amnt'].describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "501574040.5091934"
      ]
     },
     "execution_count": 107,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_EL = loan_data_EL['EL'].sum()\n",
    "total_EL"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6664052450"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "total_funded = loan_data_EL['funded_amnt'].sum()[0]\n",
    "total_funded"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.07526562017218118"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ratio_EL = total_EL / total_funded\n",
    "ratio_EL"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# --------------------------------END-----------------------------------"
   ]
  }
 ],
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