Updating Documentation

aleatory/processes/euler_maruyama/ckls_process.py

@@ -1,8 +1,37 @@
+"""Chan-Karolyi-Longstaff-Sanders (CKLS) process"""
+
 from aleatory.processes.euler_maruyama.ckls_process_generic import CKLSProcessGeneric
 from aleatory.processes import BrownianMotion, Vasicek, CIRProcess, GBM
 
 
 class CKLSProcess(CKLSProcessGeneric):
+
+    r"""
+    Chan-Karolyi-Longstaff-Sanders (CKLS) process
+
+    .. image:: _static/ckls_process_draw.png
+
+
+    A CKLS process  :math:`X = \{X : t \geq  0\}` is characterised by the following
+    Stochastic Differential Equation
+
+    .. math::
+
+      dX_t = (\alpha  + \beta X_t) dt + \sigma X_t^{\gamma} dW_t, \ \ \ \ \forall t\in (0,T],
+
+    with initial condition :math:`X_0 = x_0`, where
+
+    - :math:`\alpha \in \mathbb{R}`
+    - :math:`\beata \in \mathbb{R}`
+    - :math:`\sigma>0` is the scale of the volatility
+    - :math:`\gamma\geq 0` is the elasticity term
+    - :math:`W_t` is a standard Brownian Motion.
+
+    Reference: CHAN, K.C., KAROLYI, G.A., LONGSTAFF, F.A. and SANDERS, A.B. (1992),
+    An Empirical Comparison of Alternative Models of the Short-Term Interest Rate. The Journal of Finance,
+    47: 1209-1227. https://doi.org/10.1111/j.1540-6261.1992.tb04011.x
+
+    """
     def __new__(cls, *args, **kwargs):
         alpha = kwargs['alpha'] if  'alpha' in kwargs else 0.5
         beta = kwargs['beta'] if 'beta' in kwargs else 0.5
@@ -26,10 +55,3 @@ def __new__(cls, *args, **kwargs):
         else:
             return CKLSProcessGeneric(alpha=alpha, beta=beta, sigma=sigma, gamma=gamma, initial=initial, T=T, rng=rng)
 
-    # def __init__(self, alpha=0.5, beta=0.5, sigma=0.1, gamma=1.0, initial=1.0, T=1.0, rng=None):
-    #     super().__init__(alpha, beta, sigma, gamma, initial, T, rng)
-
-    # def __str__(self):
-    #     return "CKLS process with parameters alpha={alpha}, beta={beta}, sigma={sigma}, gamma={gamma}, initial={initial} on [0, {T}].".format(
-    #         T=str(self.T), gamma=str(self.gamma), alpha=str(self.alpha), beta=str(self.beta), sigma=str(self.sigma),
-    #         initial=self.initial)

aleatory/processes/euler_maruyama/ckls_process_generic.py

@@ -10,7 +10,7 @@ class CKLSProcessGeneric(SPEulerMaruyama):
     r"""
     Chan-Karolyi-Longstaff-Sanders (CKLS) process
 
-    .. image:: _static/cev_process_drawn.png
+    .. image:: _static/ckls_process_draw.png
 
 
     A CKLS process  :math:`X = \{X : t \geq  0\}` is characterised by the following

aleatory/processes/jump/poisson.py

@@ -1,4 +1,5 @@
 """Poisson Process"""
+
 import matplotlib.pyplot as plt
 import numpy as np
 from scipy.stats import poisson
@@ -10,6 +11,19 @@
 
 
 class PoissonProcess(BaseProcess):
+    r"""Poisson Process
+
+        .. image:: _static/poisson_process_draw.png
+
+    A Poisson point process is a type of random mathematical object that consists of points randomly located on
+    a mathematical space with the essential feature that the points occur independently of one another.
+
+    A Poisson process :math:`{N(t) : t\geq 0}` with intensity rate :math:`\lambda>0` is defined by the following properties:
+
+    1. :math:`N(t)` has a Poisson distribution with parameter :math:`\lambda t`, for each :math:`t> 0`.
+    2. It has independent increments
+
+    """
 
     def __init__(self, rate=1.0, rng=None):
         super().__init__(rng=rng)
@@ -182,4 +196,4 @@ def draw(self, N, T=None, style="seaborn-v0_8-whitegrid", colormap="RdYlBu_r", e
             plt.show()
 
         return fig
-    
+

tests/test_ckls.py

@@ -2,6 +2,26 @@
 import unittest
 
 
+def test_ckls_process():
+    name = "Chan-Karolyi-Longstaff-Sanders (CKLS) Process"
+    process = CKLSProcess(alpha=0.5, beta=1.5, sigma=0.5, gamma=0.3, initial=1.0, T=1.0)
+    # fig = process.plot(n=100, N=10, figsize=(9, 6), dpi=200, title=name)
+    # fig.savefig("ckls1.png")
+    fig = process.draw(n=100, N=300, figsize=(11, 6), dpi=200, title=name, envelope=True)
+    # fig.savefig("ckls2.png")
+    # process = CKLSProcess(alpha=0.5, beta=-2.0, sigma=0.5, gamma=0.0, initial=1.0, T=1.0)
+    # fig = process.draw(n=100, N=300, colormap="PuOr", figsize=(11, 6), dpi=200, title=name)
+    # fig.savefig("ckls3.png")
+    # process = CKLSProcess(alpha=0.0, beta=-2.0, sigma=0.5, gamma=1.0, initial=3.0, T=1.0)
+    # fig = process.draw(n=100, N=300, colormap="PiYG", figsize=(11, 6), dpi=200, title=name)
+    # fig.savefig("ckls4.png")
+    # process = CKLSProcess(alpha=0.0, beta=0.0, sigma=0.5, gamma=0.0, initial=2.0, T=1.0)
+    # fig = process.draw(n=100, N=300, colormap="Spectral", figsize=(11, 6), dpi=200, title=name)
+    # fig.savefig("ckls5.png")
+    # process.draw(n=100, N=200, envelope=False, figsize=(12, 6))
+    # process.draw(n=100, N=200, envelope=False, orientation='horizontal', figsize=(12, 6))
+    # process.draw(n=100, N=200, envelope=False, orientation='vertical', figsize=(12, 6), )
+
 class test_ckls:
     vis = False