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# Copyright (C) 2016, 2018 EDF
# All Rights Reserved
# This code is published under the GNU Lesser General Public License (GNU LGPL)
import numpy as np
import math
import random
class AR1Simulator :
# Constructor
# p_D0 Initial value
# p_m average value
# p_sigma Volatility
# p_mr Mean reverting per factor
# p_T Maturity
# p_nbStep Number of time step for simulation
# p_nbSimul Number of simulations for the Monte Carlo
# p_bForward true if the simulator is forward, false if the simulation is backward
def __init__(self, p_D0, p_m, p_sigma, p_mr, p_T, p_nbStep, p_nbSimul, p_bForward) :
self.m_D0 = p_D0
self.m_m = p_m
self.m_sigma = p_sigma
self.m_mr = p_mr
self.m_T = p_T
self.m_step = p_T / p_nbStep
self.m_nbStep = p_nbStep
self.m_nbSimul = p_nbSimul
self.m_bForward = p_bForward
self.m_currentStep = 0. if p_bForward else p_T
self.m_OUProcess = np.zeros(p_nbSimul)
np.random.seed(0)
if self.m_bForward :
self.m_OUProcess = np.zeros(p_nbSimul)
else :
stDev = self.m_sigma * math.sqrt(1 - math.exp(-2 * self.m_mr * self.m_T) / (2 * self.m_mr))
self.m_OUProcess = stDev * np.random.randn(p_nbSimul)
# a step forward for OU process
def forwardStepForOU(self) :
racine = math.sqrt((1 - np.exp(-2 * self.m_mr * self.m_currentStep)) / (2 * self.m_mr))
stDev = self.m_sigma * racine
expActu = np.exp(-self.m_mr * self.m_step)
normalSample = np.random.randn(self.m_nbSimul)
increment = np.multiply(stDev, normalSample)
# update OU process
self.m_OUProcess = np.multiply(self.m_OUProcess, expActu) + increment
# a step backward for OU process
def backwardStepForOU(self) :
if self.m_currentStep <= 0. :
self.m_OUProcess = np.zeros(self.m_nbSimul)
else :
# use brownian bridge
util = np.sinh(self.m_mr * self.m_currentStep) / np.sinh(self.m_mr * (self.m_currentStep + self.m_step))
variance = np.multiply(pow(self.m_sigma, 2.) / (np.multiply(2, self.m_mr)), (1 - np.exp(-2 * self.m_mr * self.m_currentStep)) * pow(1 - np.multiply(np.exp(-self.m_mr * self.m_step), util), 2.) + np.multiply(1 - np.exp(-2 * self.m_mr * self.m_step), pow(util, 2.)))
stdDev = np.sqrt(variance)
temp = self.m_OUProcess
self.m_OUProcess = np.multiply(temp, util) + np.multiply(stdDev, np.random.randn(self.m_nbSimul))
# get current markov state
def getParticles(self) :
ret = self.m_OUProcess + (np.zeros(len(self.m_OUProcess)) + ((self.m_D0 - self.m_m) * math.exp(- self.m_m * self.m_currentStep) + self.m_m))
retMap = np.zeros((1, len(ret)))
for i in range(len(ret)):
retMap[0,i] = max(ret[i], 0.)
return retMap
# a step forward for simulations
def stepForward(self) :
if self.m_bForward == False :
pass
else :
self.m_currentStep += self.m_step
self.forwardStepForOU()
# return the asset values (asset, simulations)
def stepBackward(self) :
if self.m_bForward == True :
pass
else :
self.m_currentStep -= self.m_step
self.backwardStepForOU()
# a step forward for simulations
# return the asset values (asset, simulations)
def stepForwardAndGetParticles(self) :
if self.m_bForward == False :
pass
else :
self.m_currentStep += self.m_step
self.forwardStepForOU()
return self.getParticles()
# a step backward for simulations
# return the asset values (asset, simulations)
def stepBackwardAndGetParticles(self) :
if self.m_bForward == True :
pass
else :
self.m_currentStep -= self.m_step
self.backwardStepForOU()
return self.getParticles()
# Get back attribute
def getCurrentStep(self) :
return self.m_currentStep
def getT(self) :
return self.m_T
def getStep(self) :
return self.m_step
def getSigma(self) :
return self.m_sigma
def getMr(self) :
return self.m_mr
def getNbSimul(self) :
return self.m_nbSimul
def getNbStep(self) :
return self.m_nbStep
def getDimension(self) :
return 1
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