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#!/usr/bin/python3
# Copyright (C) 2019 EDF
# All Rights Reserved
# This code is published under the GNU Lesser General Public License (GNU LGPL)
import numpy as np
import math
import StOptGrids
import StOptTree
import StOptGlobal
import StOptGeners
import Utils
import Simulators
import unittest
# test cases
class testAmericanOptionTest(unittest.TestCase):
def test_americanTree(self):
# define a a time grid
timeGrid = StOptGrids.OneDimRegularSpaceGrid(0., 2., 1)
# future values
futureGrid = Utils.FutureCurve(timeGrid, [50.,50.])
# degenerate trinomial tri
mr = 0.00001
sigma =0.2
# interest rate
r = 0.05
# number of time steps
nstep =50
# maturity
T =1.
# step
dt = T / nstep
# simulation dates
dates = dt * np.arange(0,nstep+1)
# simulation dates
treeSim = Simulators.TrinomialTreeOUSimulator(mr, sigma, dates)
indexT = np.arange(0,nstep+1, 5)
treeSim.dump("Tree",indexT)
# read archive
archiveToRead = StOptGeners.BinaryFileArchive("Tree", "r");
# FIRST VALORIZATION
####################
# backward simulator
backSimulator = Simulators.MeanRevertingSimulatorTree(archiveToRead, futureGrid, sigma, mr)
# strike
strike = 50.
# actu
actu = np.exp(r*dates[indexT[-1]])
# spot : add interest rate
spot = backSimulator.getSpotValues()*actu
# actualized payoff
val1= np.where( strike-spot>0,strike-spot,0)/actu
for istep in np.arange(np.shape(indexT)[0]-1):
# backward in simulator
backSimulator.stepBackward()
# get back probability matrix
proba = backSimulator.getProba()
# and connection matrix
connected = backSimulator.getConnected()
# creta tree for conditional expectation
tree=StOptTree.Tree(proba,connected)
# interest rates
actu = np.exp(r*dates[indexT[-2-istep]])
# spot : add interest rate
spot = backSimulator.getSpotValues()*actu
# pay off
payOff = np.where( strike-spot>0,strike-spot,0)/actu
# actualize value
val1 = tree.expCond(val1)
# arbitrage
val1 = np.where( val1> payOff, val1, payOff)
final = val1[0]
indexT = np.arange(0,nstep+1)
treeSim.dump("Tree",indexT)
# read archive
archiveToRead = StOptGeners.BinaryFileArchive("Tree", "r");
# backward simulator
backSimulator = Simulators.MeanRevertingSimulatorTree(archiveToRead, futureGrid, sigma, mr)
# SECOND VALORIZATION
####################
# actu
actu = np.exp(r*dates[-1])
# spot : add interest rate
spot = backSimulator.getSpotValues()*actu
# actualized payoff
val2= np.where( strike-spot>0,strike-spot,0)/actu
for istep in np.arange(nstep):
# backward in simulator
backSimulator.stepBackward()
# get back probability matrix
proba = backSimulator.getProba()
# and connection matrix
connected = backSimulator.getConnected()
# creta tree for conditional expectation
tree=StOptTree.Tree(proba,connected)
# actualize value
val2 = tree.expCond(val2)
if ((istep+1)%5==0):
# interest rates
actu = np.exp(r*dates[-2-istep])
# spot : add interest rate
spot = backSimulator.getSpotValues()*actu
# pay off
payOff = np.where( strike-spot>0,strike-spot,0)/actu
# arbitrage
val2 = np.where( val2> payOff, val2, payOff)
print("val1 " , val1 , " val2 " , val2)
self.assertAlmostEqual(val1, val2, None, None, 0.000001)
if __name__ == '__main__':
unittest.main()
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