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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 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
<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 fdmexpoujumpop.cpp
\brief Ornstein Uhlenbeck process plus jumps (Kluge Model)
*/
#include <ql/termstructures/yieldtermstructure.hpp>
#include <ql/math/interpolations/linearinterpolation.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/experimental/processes/extouwithjumpsprocess.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>
#include <ql/experimental/finitedifferences/fdmextoujumpop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/operators/secondderivativeop.hpp>
#include <ql/experimental/finitedifferences/fdmextendedornsteinuhlenbeckop.hpp>
namespace QuantLib {
FdmExtOUJumpOp::FdmExtOUJumpOp(
const boost::shared_ptr<FdmMesher>& mesher,
const boost::shared_ptr<ExtOUWithJumpsProcess>& process,
const boost::shared_ptr<YieldTermStructure>& rTS,
const FdmBoundaryConditionSet& bcSet,
Size integroIntegrationOrder)
: mesher_ (mesher),
process_(process),
rTS_ (rTS),
bcSet_ (bcSet),
gaussLaguerreIntegration_(integroIntegrationOrder),
x_ (mesher->locations(0)),
ouOp_ (new FdmExtendedOrnsteinUhlenbackOp(
mesher,
process->getExtendedOrnsteinUhlenbeckProcess(), rTS, bcSet)),
dyMap_ (FirstDerivativeOp(1, mesher)
.mult(-process->beta()*mesher->locations(1))) {
}
Size FdmExtOUJumpOp::size() const {
return mesher_->layout()->dim().size();;
}
void FdmExtOUJumpOp::setTime(Time t1, Time t2) {
ouOp_->setTime(t1, t2);
}
Disposable<Array> FdmExtOUJumpOp::apply(const Array& r) const {
return ouOp_->apply(r) + apply_direction(1, r) + integro(r);
}
Disposable<Array> FdmExtOUJumpOp::apply_mixed(const Array& r) const {
return integro(r);
}
Disposable<Array> FdmExtOUJumpOp::apply_direction(Size direction,
const Array& r) const {
if (direction == 0)
return ouOp_->apply_direction(direction, r);
else if (direction == 1)
return dyMap_.apply(r);
else {
Array retVal(r.size(), 0.0);
return retVal;
}
}
Disposable<Array>
FdmExtOUJumpOp::solve_splitting(Size direction,
const Array& r, Real a) const {
if (direction == 0) {
return ouOp_->solve_splitting(direction, r, a);
}
else if (direction == 1) {
return dyMap_.solve_splitting(r, a, 1.0);
}
else {
Array retVal(r);
return retVal;
}
}
Disposable<Array>
FdmExtOUJumpOp::preconditioner(const Array& r, Real dt) const {
return ouOp_->solve_splitting(0, r, dt);
}
FdmExtOUJumpOp::IntegroIntegrand::IntegroIntegrand(
const boost::shared_ptr<LinearInterpolation>& interpl,
const FdmBoundaryConditionSet& bcSet,
Real y, Real eta)
: y_ (y),
eta_ (eta),
bcSet_ (bcSet),
interpl_(interpl) { }
Real FdmExtOUJumpOp::IntegroIntegrand::operator()(Real u) const {
const Real y = y_ + u/eta_;
Real valueOfDerivative = interpl_->operator()(y, true);
for (FdmBoundaryConditionSet::const_iterator iter=bcSet_.begin();
iter < bcSet_.end(); ++iter) {
valueOfDerivative=(*iter)->applyAfterApplying(y, valueOfDerivative);
}
return std::exp(-u)*valueOfDerivative;
}
Disposable<Array> FdmExtOUJumpOp::integro(const Array& r) const {
Array integral(r.size());
const boost::shared_ptr<FdmLinearOpLayout> layout = mesher_->layout();
const Size extraDims=layout->size()/(layout->dim()[0]*layout->dim()[1]);
std::vector<Array> y(extraDims, Array(layout->dim()[1]));
std::vector<Matrix> f(extraDims,
Matrix(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];
const Size k = iter.index() / (layout->dim()[0]*layout->dim()[1]);
y[k][j] = mesher_->location(iter, 1);
f[k][j][i] = r[iter.index()];
}
std::vector<std::vector<boost::shared_ptr<LinearInterpolation> > >
interpl(extraDims, std::vector<
boost::shared_ptr<LinearInterpolation> >(f[0].columns()));
for (Size k=0; k < extraDims; ++k) {
for (Size i=0; i < f[k].columns(); ++i) {
interpl[k][i] = boost::shared_ptr<LinearInterpolation>(
new LinearInterpolation(y[k].begin(), y[k].end(),
f[k].column_begin(i)));
}
}
const Real eta = process_->eta();
for (FdmLinearOpIterator iter=layout->begin(); iter!=endIter; ++iter) {
const Size i = iter.coordinates()[0];
const Size j = iter.coordinates()[1];
const Size k = iter.index() / (layout->dim()[0]*layout->dim()[1]);
integral[iter.index()] = gaussLaguerreIntegration_(
IntegroIntegrand(interpl[k][i], bcSet_, y[k][j], eta));
}
return process_->jumpIntensity()*(integral-r);
}
}
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