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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
<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 fdmbatesop.cpp
\brief Bates linear operator
*/
#include <ql/methods/finitedifferences/operators/fdmbatesop.hpp>
#include <ql/processes/batesprocess.hpp>
#include <ql/quotes/simplequote.hpp>
#include <ql/math/matrix.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/termstructures/yield/zerospreadedtermstructure.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
using boost::shared_ptr;
namespace QuantLib {
FdmBatesOp::FdmBatesOp(const shared_ptr<FdmMesher>& mesher,
const shared_ptr<BatesProcess>& batesProcess,
const FdmBoundaryConditionSet& bcSet,
const Size integroIntegrationOrder,
const 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_(bcSet),
hestonOp_(new FdmHestonOp(
mesher,
shared_ptr<HestonProcess>(new HestonProcess(
batesProcess->riskFreeRate(),
Handle<YieldTermStructure>(
shared_ptr<ZeroSpreadedTermStructure>(new
ZeroSpreadedTermStructure(
batesProcess->dividendYield(),
Handle<Quote>(shared_ptr<Quote>(new SimpleQuote(lambda_*m_))),
Continuous,
NoFrequency,
batesProcess->dividendYield()->dayCounter()))),
batesProcess->s0(),
batesProcess->v0(),
batesProcess->kappa(),
batesProcess->theta(),
batesProcess->sigma(),
batesProcess->rho())),
quantoHelper)) {}
FdmBatesOp::IntegroIntegrand::IntegroIntegrand(
const 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_->operator()(x, true);
for (FdmBoundaryConditionSet::const_iterator iter=bcSet_.begin();
iter < bcSet_.end(); ++iter) {
valueOfDerivative=(*iter)->applyAfterApplying(x, valueOfDerivative);
}
return std::exp(-y*y)*valueOfDerivative;
}
Disposable<Array> FdmBatesOp::integro(const Array& r) const {
const shared_ptr<FdmLinearOpLayout> layout = mesher_->layout();
QL_REQUIRE(layout->dim().size() == 2, "invalid layout dimension");
Array x(layout->dim()[0]);
Matrix f(layout->dim()[1], layout->dim()[0]);
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter != endIter;
++iter) {
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<shared_ptr<LinearInterpolation> > interpl(f.rows());
for (Size i=0; i < f.rows(); ++i) {
interpl[i] = shared_ptr<LinearInterpolation>(
new LinearInterpolation(x.begin(), x.end(), f.row_begin(i)));
}
Array integral(r.size());
for (FdmLinearOpIterator iter=layout->begin(); iter!=endIter; ++iter) {
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);
}
}
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