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#!/usr/bin/python3
# Copyright (C) 2016 EDF
# All Rights Reserved
# This code is published under the GNU Lesser General Public License (GNU LGPL)
import math
import numpy as np
import unittest
import simulators.BlackScholesSimulator as bs
import utils.BasketOptions as bo
import StOptGrids
import StOptReg as reg
import StOptGlobal
import Simulators as sim
import Optimizers as opt
import Utils
from utils.EuropeanOptions import CallOption
from utils.EuropeanOptions import PutOption as put
import importlib
import dp.DynamicProgrammingByRegressionDist as dynmpi
accuracyClose = 0.2
accuracyNearlyEqual = 0.05
# Analytical value
# p_S asset value
# p_sigma volatility
# p_r interest rate
# p_strike strike
# p_dates possible exercise dates
# return option value
def analyticalValue(N, p_S, p_sigma, p_r, p_strike, p_dates) :
analytical = 0.
callOption = CallOption()
for i in range(len(p_dates) - N, len(p_dates)) :
analytical += callOption.operator(p_S, p_sigma, p_r, p_strike, p_dates[i])
return analytical
# Classical resolution for swing
# p_sim Monte Carlo simulator
# p_payOff Option pay off
# p_regressor regressor object
# p_dates possible exercise dates
# p_N number of exercises
def resolutionSwing(p_sim, p_payOff, p_regressor, p_dates, p_N) :
if ((p_sim.getNbStep() + 1) == len(p_dates)) == False :
pass
# asset simulated under the neutral risk probability : get the trend of first asset to get interest rate
# in this example the step between two exercises is given
expRate = p_sim.getActuStep()
# final payOff
finalPayOff = p_payOff.applyVec(p_sim.getParticles())
# Terminal function depending on simulations and stock already exercised
cashNext = np.zeros((len(finalPayOff), p_N))
for i in range(len(finalPayOff)) :
cashNext[i,:] = (finalPayOff[i]).transpose()
cashPrev = np.zeros((len(finalPayOff), p_N))
for iStep in range(len(p_dates) - 1)[::-1] :
asset = p_sim.stepBackwardAndGetParticles()
payOffLoc = p_payOff.applyVec(asset)
payOffLoc = payOffLoc.squeeze()
# conditional expectation
if iStep == 0 :
p_regressor.updateSimulations(True, asset)
else :
p_regressor.updateSimulations(False, asset)
# store conditional expectations
vecCondEspec = list(range(p_N))
for iStock in range(p_N):
vecCondEspec[iStock] = p_regressor.getAllSimulations(cashNext[:,iStock]).squeeze() * expRate
# arbitrage
for iStock in range(p_N - 1):
cashPrev[:,iStock] = np.where(payOffLoc + vecCondEspec[iStock + 1] > vecCondEspec[iStock], payOffLoc + expRate * cashNext[:,iStock + 1], expRate * cashNext[:,iStock])
# last stock
cashPrev[:,p_N - 1] = np.where(payOffLoc > vecCondEspec[p_N - 1], payOffLoc, expRate * cashNext[:,p_N - 1])
# switch
tempVec = cashNext
cashNext = cashPrev
cashPrev = tempVec
return np.mean(cashNext[:,0])
def resolutionSwingContinuation(p_sim, p_payOff, p_regressor, p_dates, p_N):
if (p_sim.getNbStep() + 1 == len(p_dates)) == False:
pass
# asset simulated under the neutral risk probability : get the trend of first asset to get interest rate
# in this example the step between two exercises is given
expRate = math.exp(-p_sim.getStep() * p_sim.getMu()[0])
lowValues = np.zeros(1)
step = np.zeros(1)
lowValues[0] = 0.
step[0] = 1
nbStep = np.zeros(1, dtype = np.int32)
nbStep[0] = p_N - 1
regular = StOptGrids.RegularSpaceGrid(lowValues, step, nbStep)
extremeGrid = np.zeros(2)
extremeGrid[0] = lowValues
extremeGrid[1] = lowValues + step * nbStep
# final payOff
finalPayOff = p_payOff.applyVec(p_sim.getParticles())
# Terminal function depending on simulations and stock already exercised
cashNext = np.zeros((len(finalPayOff), regular.getNbPoints()))
for i in range(len(finalPayOff)):
cashNext[i,:] = (np.zeros(regular.getNbPoints()) + finalPayOff[i]).transpose()
cashPrev = np.zeros((len(finalPayOff), regular.getNbPoints()))
for iStep in range(len(p_dates) - 2)[::-1] :
asset = p_sim.stepBackwardAndGetParticles()
payOffLoc = p_payOff.applyVec(asset)
# conditional expectation
if iStep == 0 :
p_regressor.updateSimulations(True, asset)
else :
p_regressor.updateSimulations(False, asset)
# continuation value object dealing with stocks
continuation = reg.ContinuationValue(regular, p_regressor, cashNext)
# iterator on grid points
iterOnGrid = regular.getGridIterator()
while iterOnGrid.isValid():
CoordStock = iterOnGrid.getCoordinate()
# use continuation to get realization of condition expectation
conditionExpecCur = np.multiply(expRate, continuation.getAllSimulations(CoordStock).squeeze())
if CoordStock[0] + 1 <= extremeGrid[1] :
conditionExpecNext = np.multiply(expRate, continuation.getAllSimulations(CoordStock + 1).squeeze())
cashPrev[:,iterOnGrid.getCount()] = np.where(payOffLoc + conditionExpecNext > conditionExpecCur, payOffLoc + np.multiply(expRate, cashNext[:,iterOnGrid.getCount() + 1]), np.multiply(expRate, cashNext[:,iterOnGrid.getCount()]))
else :
cashPrev[:,iterOnGrid.getCount()] = np.where(payOffLoc > conditionExpecCur, payOffLoc, np.multiply(expRate, cashNext[:,iterOnGrid.getCount()]))
iterOnGrid.next()
# switch pointer
tempVec = cashNext
cashNext = cashPrev
cashPrev = tempVec
return np.mean(cashNext[:,0])
# function to test stock in dimension above 1
def multiStock(p_ndim):
moduleMpi4Py=importlib.util.find_spec('mpi4py')
if (moduleMpi4Py is not None):
from mpi4py import MPI
world = MPI.COMM_WORLD
initialValues = np.zeros(1) + 1.
sigma = np.zeros(1) + 0.2
mu = np.zeros(1) + 0.05
corr = np.ones((1,1))
# number of step
nStep = 20
# exercice date
dates = np.linspace(0., 1., nStep + 1)
# exercice dates
N = 3
T = 1.
strike = 1.
nbSimul = 10000
nMesh = 4
# payoff
payoff = Utils.BasketCall(strike)
# store sequential
valueSeq = 0
# mesh
nbMesh = np.zeros(1, dtype = np.int32) + nMesh
if world.rank == 0:
# simulator
simulator = bs.BlackScholesSimulator(initialValues, sigma, mu, corr, dates[len(dates) - 1], len(dates) - 1, nbSimul, False)
# regressor
regressor = reg.LocalLinearRegression(nbMesh)
# bermudean value
valueSeq = resolutionSwing(simulator, payoff, regressor, dates, N)
# simulator
simulator = sim.BlackScholesSimulator(initialValues, sigma, mu, corr, dates[len(dates) - 1], len(dates) - 1, nbSimul, False)
# grid
lowValues = np.zeros(p_ndim)
step = np.zeros(p_ndim) + 1.
# the stock is discretized with values from 0 to N included
nbStep = np.zeros(p_ndim, dtype = np.int32) + N
grid = StOptGrids.RegularSpaceGrid(lowValues, step, nbStep)
# final value
vFunction = Utils.PayOffFictitiousSwing(payoff, N)
# optimizer
optimizer = opt.OptimizerFictitiousSwingBlackScholes(payoff, N, p_ndim)
# initial values
initialStock = np.zeros(p_ndim)
initialRegime = 0
fileToDump = "CondExpSwing"
# regressor
regressor = reg.LocalLinearRegression(nbMesh)
bOneFile = False
# link the simulations to the optimizer
optimizer.setSimulator(simulator)
valueParal = dynmpi.DynamicProgrammingByRegressionDist(grid, optimizer, regressor, vFunction, initialStock, initialRegime, fileToDump, bOneFile)
return valueParal, valueSeq
class testSwingOptionTest(unittest.TestCase) :
def test_swingOptionInOptimization(self):
initialValues = np.zeros(1) + 1.
sigma = np.zeros(1) + 0.2
mu = np.zeros(1) + 0.05
corr = np.ones((1,1))
# number of step
nStep = 30
# exercise date
dates = np.linspace(0., 1., nStep + 1)
N = 3 # 3 exercise dates
T = 1.
strike = 1.
nbSimul = 200000
nMesh = 16
# payoff
payoff = bo.BasketCall(strike)
# analytical
analytical = analyticalValue(N, initialValues[0], sigma[0], mu[0], strike, dates)
# mesh
nbMesh = np.zeros(1, dtype = np.int32) + nMesh
# simulator
simulator = bs.BlackScholesSimulator(initialValues, sigma, mu, corr, dates[len(dates) - 1], len(dates) - 1, nbSimul, False)
# regressor
regressor = reg.LocalLinearRegression(nbMesh)
# bermudean value
valueSeq = resolutionSwing(simulator, payoff, regressor, dates, N)
# simulator
simulator = bs.BlackScholesSimulator(initialValues, sigma, mu, corr, dates[len(dates) - 1], len(dates) - 1, nbSimul, False)
# regressor
regressor = reg.LocalLinearRegression(nbMesh)
# using continuation values
valueSeqContinuation = resolutionSwingContinuation(simulator, payoff, regressor, dates, N)
print("valueSeq", valueSeq, "valueSeqContinuation", valueSeqContinuation)
self.assertAlmostEqual(valueSeq, analytical, None, None, accuracyClose)
def test_swingOption2D(self):
moduleMpi4Py=importlib.util.find_spec('mpi4py')
if (moduleMpi4Py is not None):
from mpi4py import MPI
world = MPI.COMM_WORLD
val = multiStock(2)
if world.rank == 0:
self.assertAlmostEqual(val[1] * 2, val[0], None, None, accuracyNearlyEqual)
def test_swingOption3D(self):
moduleMpi4Py=importlib.util.find_spec('mpi4py')
if (moduleMpi4Py is not None):
from mpi4py import MPI
world = MPI.COMM_WORLD
val = multiStock(3)
if world.rank == 0:
self.assertAlmostEqual(val[1] * 3, val[0], None, None, accuracyNearlyEqual)
if __name__ == '__main__':
unittest.main()
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