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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2020 Lew Wei Hao
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
<http://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/fdmcirop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondordermixedderivativeop.hpp>
#include <ql/processes/blackscholesprocess.hpp>
namespace QuantLib {
FdmCIREquityPart::FdmCIREquityPart(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<GeneralizedBlackScholesProcess>& bsProcess,
Real strike)
: dxMap_ (FirstDerivativeOp(0, mesher)),
dxxMap_(SecondDerivativeOp(0, mesher)),
mapT_ (0, mesher),
mesher_(mesher),
qTS_(bsProcess->dividendYield().currentLink()),
strike_(strike),
sigma1_(bsProcess->blackVolatility().currentLink()){
}
void FdmCIREquityPart::setTime(Time t1, Time t2) {
const Rate q = qTS_->forwardRate(t1, t2, Continuous).rate();
const Real v = sigma1_->blackForwardVariance(t1, t2, strike_)/(t2-t1);
mapT_.axpyb(mesher_->locations(1) - q - 0.5*v, dxMap_,
dxxMap_.mult(Array(mesher_->layout()->size(), v/2)), -0.5*mesher_->locations(1));
}
const TripleBandLinearOp& FdmCIREquityPart::getMap() const {
return mapT_;
}
FdmCIRRatesPart::FdmCIRRatesPart(
const ext::shared_ptr<FdmMesher>& mesher,
Real sigma, Real kappa, Real theta)
: dyMap_(SecondDerivativeOp(1, mesher)
.mult(sigma*sigma*mesher->locations(1))
.add(FirstDerivativeOp(1, mesher)
.mult(kappa*(theta - mesher->locations(1))))),
mapT_(1, mesher),
mesher_(mesher){
}
void FdmCIRRatesPart::setTime(Time t1, Time t2) {
mapT_.axpyb(Array(), dyMap_, dyMap_, -0.5*mesher_->locations(1));
}
const TripleBandLinearOp& FdmCIRRatesPart::getMap() const {
return mapT_;
}
FdmCIRMixedPart::FdmCIRMixedPart(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<CoxIngersollRossProcess> & cirProcess,
const ext::shared_ptr<GeneralizedBlackScholesProcess> & bsProcess,
const Real rho,
const Real strike)
: dyMap_(SecondOrderMixedDerivativeOp(0, 1, mesher)
.mult(Array(mesher->layout()->size(), 2*rho*cirProcess->volatility()))),
mapT_(0, 1, mesher),
mesher_(mesher),
sigma1_(bsProcess->blackVolatility().currentLink()),
strike_(strike){
}
void FdmCIRMixedPart::setTime(Time t1, Time t2) {
const Real v = std::sqrt(sigma1_->blackForwardVariance(t1, t2, strike_)/(t2-t1));
NinePointLinearOp op(dyMap_.mult(Array(mesher_->layout()->size(), v)));
mapT_.swap(op);
}
const NinePointLinearOp& FdmCIRMixedPart::getMap() const {
return mapT_;
}
FdmCIROp::FdmCIROp(
const ext::shared_ptr<FdmMesher>& mesher,
const ext::shared_ptr<CoxIngersollRossProcess> & cirProcess,
const ext::shared_ptr<GeneralizedBlackScholesProcess> & bsProcess,
const Real rho,
const Real strike)
: dxMap_(mesher,
bsProcess,
strike),
dyMap_(mesher,
cirProcess->volatility(),
cirProcess->speed(),
cirProcess->level()),
dzMap_(mesher,
cirProcess,
bsProcess,
rho,
strike){
}
void FdmCIROp::setTime(Time t1, Time t2) {
dxMap_.setTime(t1, t2);
dyMap_.setTime(t1, t2);
dzMap_.setTime(t1, t2);
}
Size FdmCIROp::size() const {
return 2;
}
Disposable<Array> FdmCIROp::apply(const Array& u) const {
Array dx = dxMap_.getMap().apply(u);
Array dy = dyMap_.getMap().apply(u);
Array dz = dzMap_.getMap().apply(u);
return (dy + dx + dz);
}
Disposable<Array> FdmCIROp::apply_direction(Size direction,
const Array& r) const {
if (direction == 0)
return dxMap_.getMap().apply(r);
else if (direction == 1)
return dyMap_.getMap().apply(r);
else
QL_FAIL("direction too large");
}
Disposable<Array> FdmCIROp::apply_mixed(const Array& r) const {
return dzMap_.getMap().apply(r);
}
Disposable<Array>
FdmCIROp::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_.getMap().solve_splitting(r, a, 1.0);
}
else
QL_FAIL("direction too large");
}
Disposable<Array>
FdmCIROp::preconditioner(const Array& r, Real dt) const {
return solve_splitting(1, solve_splitting(0, r, dt), dt) ;
}
#if !defined(QL_NO_UBLAS_SUPPORT)
Disposable<std::vector<SparseMatrix> >
FdmCIROp::toMatrixDecomp() const {
std::vector<SparseMatrix> retVal(3);
retVal[0] = dxMap_.getMap().toMatrix();
retVal[1] = dyMap_.getMap().toMatrix();
retVal[2] = dzMap_.getMap().toMatrix();
return retVal;
}
#endif
}
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