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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
# Defines a fictitious swing on Ndim stocks : the valorisation will be equal to the valorisation of ndim swing
# where ndim is the number of stocks
class OptimizeFictitiousSwing:
# Constructor
# p_payoff pay off used
# p_nPointStock number of stock points
# p_ndim dimension of the problem (stock number)
# p_actu actualization factor
def __init__(self, p_payoff, p_nPointStock, p_ndim, p_actu):
self.m_payoff = p_payoff
self.m_nPointStock = p_nPointStock
self.m_ndim = p_ndim
self.m_actu = p_actu
self.m_actuStep = 1.
# define the diffusion cone for parallelism
# p_regionByProcessor region (min max) treated by the processor for the different regimes treated
# return returns in each dimension the min max values in the stock that can be reached from the grid p_gridByProcessor for each regime
def getCone(self, p_regionByProcessor):
extrGrid = np.zeros(p_regionByProcessor)
# only a single exercise
for id in range(self.m_ndim):
extrGrid[id][1] += 1.
return extrGrid
# defines a step in optimization
# Notice that this implementation is not optimal. In fact no interpolation is necessary for this asset.
# This implementation is for test and example purpose
# p_grid grid at arrival step after command
# p_stock coordinate of the stock point to treat
# p_condEsp conditional expectation operator
# p_phiIn for each regime gives the solution calculated at the previous step ( next time step by Dynamic Programming resolution)
# return for each regimes (column) gives the solution for each particle (row)
def stepOptimize(self, p_grid, p_stock, p_condEsp, p_phiIn):
nbSimul = p_condEsp[0].getNbSimul()
solutionAndControl = list(range(2))
solutionAndControl[0] = np.zeros((nbSimul, 1))
solutionAndControl[1] = np.zeros((nbSimul, 1))
payOffVal = self.m_payoff.applyVec(p_condEsp[0].getParticles())
bConstraint = False
# calculation detailed for clarity
# create interpolator at current stock point
interpolatorCurrentStock = p_grid.createInterpolator(p_stock)
# cash flow at current stock and previous step
cashSameStock = interpolatorCurrentStock.applyVec(p_phiIn[0])
# conditional expectation at current stock point
condExpSameStock = self.m_actu * p_condEsp[0].getAllSimulations(interpolatorCurrentStock)
# number of possibilities for arbitrage with m_ndim stocks
nbArb = (0x01 << self.m_ndim)
# stock to add
stockToAdd = np.zeros(self.m_ndim)
# store optimal conditional expectation
condExpOpt = np.zeros(nbSimul) - 1e6
for j in range(nbArb):
nbArb += 1
ires = j
for id in range(1, self.m_ndim + 1)[::-1]:
id -= 1
idec = (ires >> id)
stockToAdd[id] = idec
ires -= (idec << id)
p_stock = p_stock.reshape(2)
# calculation detailed for clarity
# create interpolator at next stock point accessible
nextStock = p_stock + stockToAdd
# test that stock is possible
if np.amax(nextStock) <= self.m_nPointStock:
interpolatorNextStock = p_grid.createInterpolator(nextStock)
# cash flow at next stock previous step
cashNextStock = interpolatorNextStock.applyVec(p_phiIn[0]).squeeze()
# conditional expectation at next stock
condExpNextStock = self.m_actu * p_condEsp[0].getAllSimulations(interpolatorNextStock).squeeze()
# quantity exercised
qExercized = stockToAdd.sum()
# arbitrage
condExp = payOffVal * qExercized + condExpNextStock
solutionAndControl[0][:,0] = np.where(condExp > condExpOpt, payOffVal * qExercized + self.m_actu * cashNextStock, solutionAndControl[0][:,0])
condExpOpt = np.where(condExp > condExpOpt, condExp, condExpOpt)
solutionAndControl[1][:,0] = np.where(condExp > condExpOpt, qExercized, solutionAndControl[1][:,0])
return solutionAndControl
# defines a step in simulation
# Notice that this implementation is not optimal. In fact no interpolation is necessary for this asset.
# This implementation is for test and example purpose
# p_grid grid at arrival step after command
# p_continuation defines the continuation operator for each regime
# p_state defines the state value (modified)
# p_phiInOut defines the value function (modified)
def stepSimulate(self, p_grid, p_continuation, p_state, p_phiInOut):
# number of possibilities for arbitrage with m_ndim stocks
nbArb = (0x01 << self.m_ndim)
# stock to add
stockToAdd = np.zeros(self.m_ndim)
# initialize
phiAdd = -1e6
# max of conditional expectation
expectationMax = -1e6
ptStockMax = np.zeros(len(p_state.getPtStock()))
bStock = (p_state.getPtStock()[0] == p_state.getPtStock()[1])
payOffVal = self.m_payoff.apply(p_state.getStochasticRealization())
for j in range(nbArb):
ires = j
for id in range(self.m_ndim - 1)[::-1]:
idec = (ires >> id)
stockToAdd[id] = idec
ires -= (idec << id)
nextStock = p_state.getPtStock() + stockToAdd
# test that stock is possible
if nextStock.maxCoeff() <= self.m_nPointStock:
# quantity exercised
qExercized = stockToAdd.sum()
continuationValueNext = self.m_actu * p_continuation[0].getValue(nextStock, p_state.getStochasticRealization())
expectation = payOffVal * qExercized + continuationValueNext
if (expectation > expectationMax):
ptStockMax = nextStock
phiAdd = payOffVal * qExercized * self.m_actuStep
expectationMax = expectation
p_state.setPtStock(ptStockMax)
p_phiInOut += phiAdd
# get number of regimes
def getNbRegime(self):
return 1
def getNbControl(self):
return 1
# get actualization factor
def getActuStep(self):
return self.m_actuStep
# store the simulator
def setSimulator(self, p_simulator):
self.m_simulator = p_simulator
# get the simulator back
def getSimulator(self):
return self.m_simulator
# get size of the function to follow in simulation
def getSimuFuncSize(self):
return 1
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