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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Andreas Gaida
Copyright (C) 2008 Ralph Schreyer
Copyright (C) 2008, 2011 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.
*/
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmhestonhullwhiteop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondordermixedderivativeop.hpp>
#include <ql/models/shortrate/onefactormodels/hullwhite.hpp>
#include <utility>
namespace QuantLib {
FdmHestonHullWhiteEquityPart::FdmHestonHullWhiteEquityPart(
const ext::shared_ptr<FdmMesher>& mesher,
ext::shared_ptr<HullWhite> hwModel,
ext::shared_ptr<YieldTermStructure> qTS)
: x_(mesher->locations(2)), varianceValues_(0.5 * mesher->locations(1)),
dxMap_(FirstDerivativeOp(0, mesher)),
dxxMap_(SecondDerivativeOp(0, mesher).mult(0.5 * mesher->locations(1))), mapT_(0, mesher),
hwModel_(std::move(hwModel)), mesher_(mesher), qTS_(std::move(qTS)) {
// on the boundary s_min and s_max the second derivative
// d²V/dS² is zero and due to Ito's Lemma the variance term
// in the drift should vanish.
for (const auto& iter : *mesher_->layout()) {
if ( iter.coordinates()[0] == 0
|| iter.coordinates()[0] == mesher_->layout()->dim()[0]-1) {
varianceValues_[iter.index()] = 0.0;
}
}
volatilityValues_ = Sqrt(2*varianceValues_);
}
void FdmHestonHullWhiteEquityPart::setTime(Time t1, Time t2) {
const ext::shared_ptr<OneFactorModel::ShortRateDynamics> dynamics =
hwModel_->dynamics();
const Real phi = 0.5*( dynamics->shortRate(t1, 0.0)
+ dynamics->shortRate(t2, 0.0));
const Rate q = qTS_->forwardRate(t1, t2, Continuous).rate();
mapT_.axpyb(x_+phi-varianceValues_-q, dxMap_, dxxMap_, Array());
}
const TripleBandLinearOp& FdmHestonHullWhiteEquityPart::getMap() const {
return mapT_;
}
FdmHestonHullWhiteOp::FdmHestonHullWhiteOp(const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<HestonProcess>& hestonProcess,
const ext::shared_ptr<HullWhiteProcess>& hwProcess,
Real equityShortRateCorrelation)
: v0_(hestonProcess->v0()), kappa_(hestonProcess->kappa()), theta_(hestonProcess->theta()),
sigma_(hestonProcess->sigma()), rho_(hestonProcess->rho()),
hwModel_(ext::make_shared<HullWhite>(
hestonProcess->riskFreeRate(), hwProcess->a(), hwProcess->sigma())),
hestonCorrMap_(
SecondOrderMixedDerivativeOp(0, 1, mesher).mult(rho_ * sigma_ * mesher->locations(1))),
equityIrCorrMap_(
SecondOrderMixedDerivativeOp(0, 2, mesher)
.mult(Sqrt(mesher->locations(1)) * hwProcess->sigma() * equityShortRateCorrelation)),
dyMap_(SecondDerivativeOp(1U, mesher)
.mult(0.5 * sigma_ * sigma_ * mesher->locations(1))
.add(FirstDerivativeOp(1, mesher).mult(kappa_ * (theta_ - mesher->locations(1))))),
dxMap_(mesher, hwModel_, hestonProcess->dividendYield().currentLink()),
hullWhiteOp_(mesher, hwModel_, 2) {
QL_REQUIRE( equityShortRateCorrelation*equityShortRateCorrelation
+ hestonProcess->rho()*hestonProcess->rho() <= 1.0,
"correlation matrix has negative eigenvalues");
}
void FdmHestonHullWhiteOp::setTime(Time t1, Time t2) {
dxMap_.setTime(t1, t2);
hullWhiteOp_.setTime(t1, t2);
}
Size FdmHestonHullWhiteOp::size() const {
return 3;
}
Array FdmHestonHullWhiteOp::apply(const Array& u) const {
return dyMap_.apply(u) + dxMap_.getMap().apply(u)
+ hullWhiteOp_.apply(u)
+ hestonCorrMap_.apply(u) + equityIrCorrMap_.apply(u);
}
Array FdmHestonHullWhiteOp::apply_direction(Size direction,
const Array& r) const {
if (direction == 0)
return dxMap_.getMap().apply(r);
else if (direction == 1)
return dyMap_.apply(r);
else if (direction == 2)
return hullWhiteOp_.apply(r);
else
QL_FAIL("direction too large");
}
Array FdmHestonHullWhiteOp::apply_mixed(const Array& r) const {
return hestonCorrMap_.apply(r) + equityIrCorrMap_.apply(r);
}
Array FdmHestonHullWhiteOp::solve_splitting(Size direction, const Array& r,
Real a) const {
if (direction == 0) {
return dxMap_.getMap().solve_splitting(r, a, 1.0);
}
else if (direction == 1) {
return dyMap_.solve_splitting(r, a, 1.0);
}
else if (direction == 2) {
return hullWhiteOp_.solve_splitting(2, r, a);
}
else
QL_FAIL("direction too large");
}
Array FdmHestonHullWhiteOp::preconditioner(const Array& r,
Real dt) const {
return solve_splitting(0, r, dt);
}
std::vector<SparseMatrix> FdmHestonHullWhiteOp::toMatrixDecomp() const {
return {
dxMap_.getMap().toMatrix(),
dyMap_.toMatrix(),
hullWhiteOp_.toMatrixDecomp().front(),
hestonCorrMap_.toMatrix() + equityIrCorrMap_.toMatrix()
};
}
}
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