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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2010 Klaus Spanderen
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.
*/
/*! \file fdmbatesop.cpp
\brief Bates linear operator
*/
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/math/matrix.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmbatesop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/utilities/fdmdirichletboundary.hpp>
#include <ql/processes/batesprocess.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/termstructures/yield/zerospreadedtermstructure.hpp>
#include <utility>
namespace QuantLib {
FdmBatesOp::FdmBatesOp(const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<BatesProcess>& batesProcess,
FdmBoundaryConditionSet bcSet,
const Size integroIntegrationOrder,
const ext::shared_ptr<FdmQuantoHelper>& quantoHelper)
: lambda_(batesProcess->lambda()), delta_(batesProcess->delta()), nu_(batesProcess->nu()),
m_(std::exp(nu_ + 0.5 * delta_ * delta_) - 1.0),
gaussHermiteIntegration_(integroIntegrationOrder), mesher_(mesher), bcSet_(std::move(bcSet)),
hestonOp_(new FdmHestonOp(
mesher,
ext::make_shared<HestonProcess>(
batesProcess->riskFreeRate(),
Handle<YieldTermStructure>(ext::make_shared<ZeroSpreadedTermStructure>(
batesProcess->dividendYield(),
Handle<Quote>(ext::shared_ptr<Quote>(new SimpleQuote(lambda_ * m_))),
Continuous)),
batesProcess->s0(),
batesProcess->v0(),
batesProcess->kappa(),
batesProcess->theta(),
batesProcess->sigma(),
batesProcess->rho()),
quantoHelper)) {}
FdmBatesOp::IntegroIntegrand::IntegroIntegrand(
const ext::shared_ptr<LinearInterpolation>& interpl,
const FdmBoundaryConditionSet& bcSet,
Real x, Real delta, Real nu)
: x_(x), delta_(delta), nu_(nu),
bcSet_(bcSet), interpl_(interpl) { }
Real FdmBatesOp::IntegroIntegrand::operator()(Real y) const {
const Real x = x_ + M_SQRT2*delta_*y + nu_;
Real valueOfDerivative = (*interpl_)(x, true);
for (auto iter = bcSet_.begin(); iter < bcSet_.end(); ++iter) {
const ext::shared_ptr<FdmDirichletBoundary> dirichlet
= ext::dynamic_pointer_cast<FdmDirichletBoundary>(*iter);
QL_REQUIRE(dirichlet, "FdmBatesOp can only deal with Dirichlet "
"boundary conditions.");
valueOfDerivative
= dirichlet->applyAfterApplying(x, valueOfDerivative);
}
return std::exp(-y*y)*valueOfDerivative;
}
Array FdmBatesOp::integro(const Array& r) const {
QL_REQUIRE(mesher_->layout()->dim().size() == 2, "invalid layout dimension");
Array x(mesher_->layout()->dim()[0]);
Matrix f(mesher_->layout()->dim()[1], mesher_->layout()->dim()[0]);
for (const auto& iter : *mesher_->layout()) {
const Size i = iter.coordinates()[0];
const Size j = iter.coordinates()[1];
x[i] = mesher_->location(iter, 0);
f[j][i] = r[iter.index()];
}
std::vector<ext::shared_ptr<LinearInterpolation> > interpl(f.rows());
for (Size i=0; i < f.rows(); ++i) {
interpl[i] = ext::make_shared<LinearInterpolation>(
x.begin(), x.end(), f.row_begin(i));
}
Array integral(r.size());
for (const auto& iter : *mesher_->layout()) {
const Size i = iter.coordinates()[0];
const Size j = iter.coordinates()[1];
integral[iter.index()] = M_1_SQRTPI*
gaussHermiteIntegration_(
IntegroIntegrand(interpl[j], bcSet_, x[i], delta_, nu_));
}
return lambda_*(integral-r);
}
std::vector<SparseMatrix> FdmBatesOp::toMatrixDecomp() const {
QL_FAIL("not implemented");
}
}
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