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# Copyright (C) 2016 EDF
# All Rights Reserved
# This code is published under the GNU Lesser General Public License (GNU LGPL)
import numpy as np
import math as maths
# american option by Longstaff-Schwartz
# p_sim Monte Carlo simulator
# p_payOff Option pay off
# p_regressor regressor object
def resolution(p_simulator, p_payOff, p_regressor) :
step = p_simulator.getStep()
# asset simulated under the neutral risk probability : get the trend of first asset to get interest rate
expRate = np.exp(-step * p_simulator.getMu()[0])
# Terminal
particle = p_simulator.getParticles()
Cash = p_payOff.operator(particle)
for iStep in range(0, p_simulator.getNbStep()):
asset = p_simulator.stepBackwardAndGetParticles()
payOffLoc = p_payOff.operator(asset)
isLastStep = False
if iStep == p_simulator.getNbStep() - 1 :
isLastStep = True
p_regressor.updateSimulations(isLastStep, asset)
# conditional expectation
condEspec = p_regressor.getAllSimulations(Cash).squeeze() * expRate
# arbitrage
Cash = np.where(condEspec < payOffLoc, payOffLoc, Cash * expRate)
return maths.fsum(Cash) / len(Cash)
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