Finish p3, p4

HW03_2019_09_30/p1.aux

@@ -0,0 +1 @@
+\relax 

HW03_2019_09_30/p1.fdb_latexmk

@@ -0,0 +1,25 @@
+# Fdb version 3
+["pdflatex"] 1570211777 "/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.tex" "/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.pdf" "p1" 1570211777
+  "/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.aux" 1570211777 8 a94a2480d3289e625eea47cd1b285758 ""
+  "/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.tex" 1570211777 247 8071d3c5f16d933e933ba95d6076a45e ""
+  "/usr/local/texlive/2019/texmf-dist/fonts/map/fontname/texfonts.map" 1511824771 3332 103109f5612ad95229751940c61aada0 ""
+  "/usr/local/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm" 1136768653 1324 c910af8c371558dc20f2d7822f66fe64 ""
+  "/usr/local/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr12.tfm" 1136768653 1288 655e228510b4c2a1abe905c368440826 ""
+  "/usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb" 1248133631 32080 340ef9bf63678554ee606688e7b5339d ""
+  "/usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb" 1248133631 36299 5f9df58c2139e7edcf37c8fca4bd384d ""
+  "/usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb" 1248133631 35752 024fb6c41858982481f6968b5fc26508 ""
+  "/usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb" 1248133631 32762 224316ccc9ad3ca0423a14971cfa7fc1 ""
+  "/usr/local/texlive/2019/texmf-dist/tex/latex/base/article.cls" 1544567569 19933 3097d1b31d3c45dc957096f554529032 ""
+  "/usr/local/texlive/2019/texmf-dist/tex/latex/base/size10.clo" 1544567569 8294 6d6e23d5169c0d89d173f6c7e08a005a ""
+  "/usr/local/texlive/2019/texmf-dist/web2c/texmf.cnf" 1566248362 39543 a0bd1f17d0daea30a3905c0b020d0959 ""
+  "/usr/local/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map" 1566642953 4641080 fe1b79c6ead19573b2061dde83f2c777 ""
+  "/usr/local/texlive/2019/texmf-var/web2c/pdftex/pdflatex.fmt" 1566643052 4264881 087ad6a495ffe58ae3a112c69127d905 ""
+  "/usr/local/texlive/2019/texmf.cnf" 1557341546 577 d150fef99ac436ad1156e86b0892f6ef ""
+  "p1.aux" 1570211777 8 a94a2480d3289e625eea47cd1b285758 "pdflatex"
+  "p1.tex" 1570211777 247 8071d3c5f16d933e933ba95d6076a45e ""
+  (generated)
+  "/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.pdf"
+  "p1.aux"
+  "p1.log"
+  "/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.log"
+  "p1.pdf"

HW03_2019_09_30/p1.fls

@@ -0,0 +1,23 @@
+PWD /Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30
+INPUT /usr/local/texlive/2019/texmf.cnf
+INPUT /usr/local/texlive/2019/texmf-dist/web2c/texmf.cnf
+INPUT /usr/local/texlive/2019/texmf-var/web2c/pdftex/pdflatex.fmt
+INPUT /Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.tex
+OUTPUT /Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.log
+INPUT /usr/local/texlive/2019/texmf-dist/tex/latex/base/article.cls
+INPUT /usr/local/texlive/2019/texmf-dist/tex/latex/base/article.cls
+INPUT /usr/local/texlive/2019/texmf-dist/tex/latex/base/size10.clo
+INPUT /usr/local/texlive/2019/texmf-dist/tex/latex/base/size10.clo
+INPUT /Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.aux
+INPUT /Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.aux
+OUTPUT /Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.aux
+INPUT /usr/local/texlive/2019/texmf-dist/fonts/map/fontname/texfonts.map
+INPUT /usr/local/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmr12.tfm
+INPUT /usr/local/texlive/2019/texmf-dist/fonts/tfm/public/cm/cmbx12.tfm
+OUTPUT /Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.pdf
+INPUT /usr/local/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map
+INPUT /Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.aux
+INPUT /usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb
+INPUT /usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb
+INPUT /usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb
+INPUT /usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb

HW03_2019_09_30/p1.log

@@ -0,0 +1,62 @@
+This is pdfTeX, Version 3.14159265-2.6-1.40.20 (TeX Live 2019) (preloaded format=pdflatex 2019.8.24)  4 OCT 2019 19:56
+entering extended mode
+ restricted \write18 enabled.
+ file:line:error style messages enabled.
+ %&-line parsing enabled.
+**"/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.tex"
+(/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.tex
+LaTeX2e <2018-12-01>
+(/usr/local/texlive/2019/texmf-dist/tex/latex/base/article.cls
+Document Class: article 2018/09/03 v1.4i Standard LaTeX document class
+(/usr/local/texlive/2019/texmf-dist/tex/latex/base/size10.clo
+File: size10.clo 2018/09/03 v1.4i Standard LaTeX file (size option)
+)
+\c@part=\count80
+\c@section=\count81
+\c@subsection=\count82
+\c@subsubsection=\count83
+\c@paragraph=\count84
+\c@subparagraph=\count85
+\c@figure=\count86
+\c@table=\count87
+\abovecaptionskip=\skip41
+\belowcaptionskip=\skip42
+\bibindent=\dimen102
+) (/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.aux)
+\openout1 = `p1.aux'.
+
+LaTeX Font Info:    Checking defaults for OML/cmm/m/it on input line 2.
+LaTeX Font Info:    ... okay on input line 2.
+LaTeX Font Info:    Checking defaults for T1/cmr/m/n on input line 2.
+LaTeX Font Info:    ... okay on input line 2.
+LaTeX Font Info:    Checking defaults for OT1/cmr/m/n on input line 2.
+LaTeX Font Info:    ... okay on input line 2.
+LaTeX Font Info:    Checking defaults for OMS/cmsy/m/n on input line 2.
+LaTeX Font Info:    ... okay on input line 2.
+LaTeX Font Info:    Checking defaults for OMX/cmex/m/n on input line 2.
+LaTeX Font Info:    ... okay on input line 2.
+LaTeX Font Info:    Checking defaults for U/cmr/m/n on input line 2.
+LaTeX Font Info:    ... okay on input line 2.
+LaTeX Font Info:    External font `cmex10' loaded for size
+(Font)              <7> on input line 4.
+LaTeX Font Info:    External font `cmex10' loaded for size
+(Font)              <5> on input line 4.
+ [1
+
+{/usr/local/texlive/2019/texmf-var/fonts/map/pdftex/updmap/pdftex.map}] (/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.aux) ) 
+Here is how much of TeX's memory you used:
+ 208 strings out of 492609
+ 2893 string characters out of 6129048
+ 59806 words of memory out of 5000000
+ 4212 multiletter control sequences out of 15000+600000
+ 4245 words of font info for 16 fonts, out of 8000000 for 9000
+ 1141 hyphenation exceptions out of 8191
+ 23i,4n,17p,206b,109s stack positions out of 5000i,500n,10000p,200000b,80000s
+</usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/local/texlive/2019/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb>
+Output written on "/Users/YuhouZhou/Desktop/2019 Fall/Stochastic_Method/sml_2019/HW03_2019_09_30/p1.pdf" (1 page, 33603 bytes).
+PDF statistics:
+ 24 PDF objects out of 1000 (max. 8388607)
+ 16 compressed objects within 1 object stream
+ 0 named destinations out of 1000 (max. 500000)
+ 1 words of extra memory for PDF output out of 10000 (max. 10000000)
+

HW03_2019_09_30/p1.tex

@@ -0,0 +1,10 @@
+\documentclass{article}
+\begin{document}
+    \section*{Problem 1 Answer}
+    \begin{equation}
+        \omega_{1} + \omega_{2} = 1
+    \end{equation}
+    \begin{equation}
+        \omega_{1}D_{1}+\omega_{2}D_{2} = D
+    \end{equation}
+\end{document}

HW03_2019_09_30/p3.py

@@ -0,0 +1,43 @@
+import numpy as np
+import matplotlib.pyplot as plt
+
+
+def payoff(s, x, type, position):
+    """
+
+    :param s: float. stock price
+    :param x: float. strike price
+    :param type: str. type of options. 'put' or 'call'
+    :param psotion: str. 'long' position or 'short' position
+    :return: payoff
+    """
+    zero = np.zeros(len(s))
+    if type == 'call' and position == 'long':
+        return np.fmax(zero, s - x)
+    elif type == 'put' and position == 'long':
+        return np.fmax(zero, x - s)
+    elif type == 'call' and position == 'short':
+        return np.fmin(zero, x - s)
+    elif type == 'put' and position == 'short':
+        return np.fmin(zero, s - x)
+    else:
+        print('Invalid input!')
+
+
+if __name__ == '__main__':
+    s = np.arange(0, 200)
+    x = 100
+    types = ['call', 'put']
+    positions = ['long', 'short']
+    i = 0
+    for type in types:
+        for position in  positions:
+            i += 1
+            plt.subplot(len(types), len(positions), i)
+            plt.plot(s, payoff(s=s, x=x, type=type, position=position))
+            plt.title(position + ' a ' + type)
+            plt.ylabel('Payoff')
+            plt.xlabel('Price')
+    plt.tight_layout()
+    plt.savefig('p3.pdf')
+    plt.show()

HW03_2019_09_30/p4.py

@@ -0,0 +1,15 @@
+from p3 import payoff
+import numpy as np
+import matplotlib.pyplot as plt
+
+if __name__ == '__main__':
+    s = np.arange(30, 110)
+    payoff_butterfly = payoff(s=s, x=50, type='call', position='long') +\
+                       payoff(s=s, x=90, type='call', position='long') + \
+                       payoff(s=s, x=70, type='call', position='short') * 2
+    plt.plot(s, payoff_butterfly)
+    plt.xlabel('Stock Price [$]')
+    plt.ylabel('Payoff [$]')
+    plt.title('Butterfly Spread')
+    plt.savefig('p4.pdf')
+    plt.show()