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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2006 Mark Joshi
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<https://www.quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
#include <ql/methods/montecarlo/genericlsregression.hpp>
#include <ql/math/statistics/sequencestatistics.hpp>
#include <ql/math/matrixutilities/svd.hpp>
namespace QuantLib {
Real genericLongstaffSchwartzRegression(
std::vector<std::vector<NodeData> >& simulationData,
std::vector<std::vector<Real> >& basisCoefficients) {
Size steps = simulationData.size();
basisCoefficients.resize(steps-1);
for (Size i=steps-1; i!=0; --i) {
std::vector<NodeData>& exerciseData = simulationData[i];
// 1) find the covariance matrix of basis function values and
// deflated cash-flows
Size N = exerciseData.front().values.size();
std::vector<Real> temp(N+1);
SequenceStatistics stats(N+1);
Size j;
for (j=0; j<exerciseData.size(); ++j) {
if (exerciseData[j].isValid) {
std::copy(exerciseData[j].values.begin(),
exerciseData[j].values.end(),
temp.begin());
temp.back() = exerciseData[j].cumulatedCashFlows
- exerciseData[j].controlValue;
stats.add(temp);
}
}
std::vector<Real> means = stats.mean();
Matrix covariance = stats.covariance();
Matrix C(N,N);
Array target(N);
for (Size k=0; k<N; ++k) {
target[k] = covariance[k][N] + means[k]*means[N];
for (Size l=0; l<=k; ++l)
C[k][l] = C[l][k] = covariance[k][l] + means[k]*means[l];
}
// 2) solve for least squares regression
Array alphas = SVD(C).solveFor(target);
basisCoefficients[i-1].resize(N);
std::copy(alphas.begin(), alphas.end(),
basisCoefficients[i-1].begin());
// 3) use exercise strategy to divide paths into exercise and
// non-exercise domains
for (j=0; j<exerciseData.size(); ++j) {
if (exerciseData[j].isValid) {
Real exerciseValue = exerciseData[j].exerciseValue;
Real continuationValue =
exerciseData[j].cumulatedCashFlows;
Real estimatedContinuationValue =
std::inner_product(
exerciseData[j].values.begin(),
exerciseData[j].values.end(),
alphas.begin(),
exerciseData[j].controlValue);
// for exercise paths, add deflated rebate to
// deflated cash-flows at previous time frame;
// for non-exercise paths, add deflated cash-flows to
// deflated cash-flows at previous time frame
Real value = estimatedContinuationValue <= exerciseValue ?
exerciseValue :
continuationValue;
simulationData[i-1][j].cumulatedCashFlows += value;
}
}
}
// the value of the product can now be estimated by averaging
// over all paths
Statistics estimate;
std::vector<NodeData>& estimatedData = simulationData[0];
for (auto& j : estimatedData)
estimate.add(j.cumulatedCashFlows);
return estimate.mean();
}
}
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