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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2012, 2013 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
<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.
*/
/*! \file fdmhestonfwdop.cpp
*/
#include <ql/processes/hestonprocess.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/firstderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/methods/finitedifferences/operators/secondordermixedderivativeop.hpp>
#include <ql/experimental/finitedifferences/fdmhestonfwdop.hpp>
#include <ql/experimental/finitedifferences/modtriplebandlinearop.hpp>
namespace QuantLib {
FdmHestonFwdOp::FdmHestonFwdOp(
const boost::shared_ptr<FdmMesher>& mesher,
const boost::shared_ptr<HestonProcess>& process)
: kappa_(process->kappa()),
theta_(process->theta()),
sigma_(process->sigma()),
rho_ (process->rho()),
v0_ (process->v0()),
rTS_ (process->riskFreeRate().currentLink()),
qTS_ (process->dividendYield().currentLink()),
varianceValues_(0.5*mesher->locations(1)),
dxMap_ (new FirstDerivativeOp(0, mesher)),
dxxMap_(new ModTripleBandLinearOp(TripleBandLinearOp(
SecondDerivativeOp(0, mesher).mult(0.5*mesher->locations(1))))),
mapX_ (new TripleBandLinearOp(0, mesher)),
mapY_ (new FdmSquareRootFwdOp(mesher,kappa_,theta_,sigma_, 1)),
correlation_(new NinePointLinearOp(
SecondOrderMixedDerivativeOp(0, 1, mesher)
.mult(rho_*sigma_*mesher->locations(1))))
{
const boost::shared_ptr<FdmLinearOpLayout> layout = mesher->layout();
// zero flux boundary condition
const Size n = layout->dim()[1];
const Real alpha = 2*rho_*mapY_->v(0)/sigma_*mapY_->f0();
const Real beta = 2*rho_*mapY_->v(n)/sigma_*mapY_->f1();
ModTripleBandLinearOp fDx(FirstDerivativeOp(0, mesher));
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter != endIter;
++iter) {
if (iter.coordinates()[1] == 0) {
const Size idx = iter.index();
dxxMap_->upper()[idx]+= alpha*fDx.upper()[idx];
dxxMap_->diag()[idx] += alpha*fDx.diag()[idx];
dxxMap_->lower()[idx] += alpha*fDx.lower()[idx];
}
else if (iter.coordinates()[1] == n-1) {
const Size idx = iter.index();
dxxMap_->upper()[idx]+= beta*fDx.upper()[idx];
dxxMap_->diag()[idx] += beta*fDx.diag()[idx];
dxxMap_->lower()[idx] += beta*fDx.lower()[idx];
}
}
}
Size FdmHestonFwdOp::size() const {
return 2;
}
void FdmHestonFwdOp::setTime(Time t1, Time t2){
const Rate r = rTS_->forwardRate(t1, t2, Continuous).rate();
const Rate q = qTS_->forwardRate(t1, t2, Continuous).rate();
mapX_->axpyb( - r + q + rho_*sigma_ + varianceValues_, *dxMap_,
*dxxMap_, Array());
}
Disposable<Array> FdmHestonFwdOp::apply(const Array& u) const {
return mapX_->apply(u)
+ mapY_->apply(u)
+ correlation_->apply(u);
}
Disposable<Array> FdmHestonFwdOp::apply_mixed(const Array& u) const{
return correlation_->apply(u);
}
Disposable<Array> FdmHestonFwdOp::apply_direction(
Size direction, const Array& u) const {
if (direction == 0)
return mapX_->apply(u) ;
else if (direction == 1)
return mapY_->apply(u) ;
else
QL_FAIL("direction too large");
}
Disposable<Array> FdmHestonFwdOp::solve_splitting(
Size direction, const Array& u, Real s) const{
if (direction == 0) {
return mapX_->solve_splitting(u, s, 1.0);
}
else if (direction == 1) {
return mapY_->solve_splitting(1, u, s);
}
else
QL_FAIL("direction too large");
}
Disposable<Array> FdmHestonFwdOp::preconditioner(
const Array& u, Real dt) const{
return solve_splitting(0, u, dt);
}
#if !defined(QL_NO_UBLAS_SUPPORT)
Disposable<std::vector<SparseMatrix> > FdmHestonFwdOp::toMatrixDecomp()
const {
std::vector<SparseMatrix> retVal(3);
retVal[0] = mapX_->toMatrix();
retVal[1] = mapY_->toMatrix();
retVal[2] = correlation_->toMatrix();
return retVal;
}
#endif
}
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