From c1609f272d3a5f7f4db59bdb2dd175d6d6b992da Mon Sep 17 00:00:00 2001
From: "nhaga5@gmail.com" <nhaga5@gmail.com>
Date: Tue, 4 Feb 2020 00:44:20 +0000
Subject: [PATCH] added some stochastic processes

---
 docs/stochastic_processes.rst | 131 ++++++++++++++++++++++++++++++++++
 1 file changed, 131 insertions(+)

diff --git a/docs/stochastic_processes.rst b/docs/stochastic_processes.rst
index 99d6231..071890d 100644
--- a/docs/stochastic_processes.rst
+++ b/docs/stochastic_processes.rst
@@ -35,27 +35,127 @@ BlackScholesProcess
 BlackScholesMertonProcess
 #########################
 
+.. function:: ql.BlackScholesMertonProcess(initialValue, dividendTS, riskFreeTS, volTS)
+
+.. code-block:: python
+
+  initialValue = ql.QuoteHandle(ql.SimpleQuote(100))
+  sigma = 0.2
+  today = ql.Date().todaysDate()
+  riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
+  dividendTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.01, ql.Actual365Fixed()))
+  volTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(today, ql.NullCalendar(), sigma, ql.Actual365Fixed()))
+  process = ql.BlackScholesMertonProcess(initialValue, dividendTS, riskFreeTS, volTS)
+
+
 GeneralizedBlackScholesProcess
 ##############################
 
+.. function:: ql.GeneralizedBlackScholesProcess(initialValue, dividendTS, riskFreeTS, volTS)
+
+.. code-block:: python
+
+  initialValue = ql.QuoteHandle(ql.SimpleQuote(100))
+  sigma = 0.2
+  today = ql.Date().todaysDate()
+  riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
+  dividendTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.01, ql.Actual365Fixed()))
+  volTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(today, ql.NullCalendar(), sigma, ql.Actual365Fixed()))
+  process = ql.GeneralizedBlackScholesProcess(initialValue, dividendTS, riskFreeTS, volTS)
+
+
+
 ExtendedOrnsteinUhlenbeckProcess
 ################################
 
+.. function:: ql.ExtendedOrnsteinUhlenbeckProcess(speed, sigma, x0)
+
+.. code-block:: python
+
+  x0 = 0.0
+  speed = 1.0
+  volatility = 0.1
+  process = ql.ExtendedOrnsteinUhlenbeckProcess(speed, volatility, x0, lambda x: x0)
+
+
 ExtOUWithJumpsProcess
 #####################
 
+.. code-block:: python
+
+  x0 = 0.0
+  x1 = 0.0
+  beta = 4.0
+  eta = 4.0
+  jumpIntensity = 1.0
+  speed = 1.0
+  volatility = 0.1
+  ouProcess = ql.ExtendedOrnsteinUhlenbeckProcess(speed, volatility, x0, lambda x: x0)
+  process = ql.ExtOUWithJumpsProcess(ouProcess, x1, beta, jumpIntensity, eta)
+
 BlackProcess
 ############
 
+.. function:: ql.BlackProcess(initialValue, riskFreeTS, volTS)
+
+.. code-block:: python
+
+  initialValue = ql.QuoteHandle(ql.SimpleQuote(100))
+  sigma = 0.2
+  today = ql.Date().todaysDate()
+  riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
+  volTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(today, ql.NullCalendar(), sigma, ql.Actual365Fixed()))
+  process = ql.BlackProcess(initialValue, riskFreeTS, volTS)
+
+
 Merton76Process
 ###############
 
+.. code-block:: python
+
+  initialValue = ql.QuoteHandle(ql.SimpleQuote(100))
+  sigma = 0.2
+  today = ql.Date().todaysDate()
+  dividendTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.01, ql.Actual365Fixed()))
+
+  riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
+  volTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(today, ql.NullCalendar(), sigma, ql.Actual365Fixed()))
+  process = ql.BlackProcess(initialValue, riskFreeTS, volTS)
+
+  jumpIntensity = ql.QuoteHandle(ql.SimpleQuote(1.0))
+  jumpVolatility = ql.QuoteHandle(ql.SimpleQuote(sigma * np.sqrt(0.25 / jumpIntensity.value())))
+  meanLogJump = ql.QuoteHandle(ql.SimpleQuote(-jumpVolatility.value()*jumpVolatility.value()))
+
+  process = ql.Merton76Process(initialValue, dividendTS, riskFreeTS, volTS, jumpIntensity, meanLogJump, jumpVolatility)
+
 VarianceGammaProcess
 ####################
 
+.. code-block:: python
+
+  initialValue = ql.QuoteHandle(ql.SimpleQuote(100))
+  riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
+  dividendTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.01, ql.Actual365Fixed()))
+
+  sigma = 0.2
+  nu = 1
+  theta = 1
+  process = ql.VarianceGammaProcess(initialValue, dividendTS, riskFreeTS, sigma, nu, theta)
+
 GarmanKohlagenProcess
 #####################
 
+.. function:: ql.GarmanKohlagenProcess(initialValue, foreignRiskFreeTS, domesticRiskFreeTS, volTS)
+
+.. code-block:: python
+
+initialValue = ql.QuoteHandle(ql.SimpleQuote(100))
+domesticRiskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.03, ql.Actual365Fixed()))
+foreignRiskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.01, ql.Actual365Fixed()))
+volTS = ql.BlackVolTermStructureHandle(ql.BlackConstantVol(today, ql.NullCalendar(), sigma, ql.Actual365Fixed()))
+process = ql.GarmanKohlagenProcess(initialValue, foreignRiskFreeTS, domesticRiskFreeTS, volTS)
+
+
 HestonProcess
 #############
 
@@ -65,12 +165,43 @@ BatesProcess
 HullWhiteProcess
 ################
 
+.. function:: ql.HullWhiteProcess(riskFreeTS, a, sigma)
+
+.. code-block:: python
+
+  riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
+  a = 0.001
+  sigma = 0.1
+  process = ql.HullWhiteProcess(riskFreeTS, a, sigma)
+
+
 HullWhiteForwardProcess
 #######################
 
+.. function:: ql.HullWhiteForwardProcess(riskFreeTS, a, sigma)
+
+.. code-block:: python
+
+riskFreeTS = ql.YieldTermStructureHandle(ql.FlatForward(today, 0.05, ql.Actual365Fixed()))
+a = 0.001
+sigma = 0.1
+process = ql.HullWhiteForwardProcess(riskFreeTS, a, sigma)
+
+
 GSR Process
 ###########
 
+.. code-block:: python
+
+  today = ql.Date().todaysDate()
+  dates = [ql.TARGET().advance(today, ql.Period(i, ql.Days)) for i in range(1,10)]
+  times = [i for i in range(1,10)]
+  sigmas = [0.01 for i in range(0, len(dates)+1)]
+  reversion = 0.01
+  reversions = [reversion]
+  process = ql.GsrProcess(times, sigmas, reversions)
+
+
 G2Process
 #########