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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 fdsimpleextoustorageengine.cpp
\brief Finite Differences extended OU engine for simple storage options
*/
#include <ql/termstructures/yieldtermstructure.hpp>
#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/meshers/fdmsimpleprocess1dmesher.hpp>
#include <ql/pricingengines/vanilla/fdsimplebsswingengine.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsimplestoragecondition.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/experimental/finitedifferences/fdsimpleextoustorageengine.hpp>
#include <ql/methods/finitedifferences/solvers/fdmsolverdesc.hpp>
#include <ql/methods/finitedifferences/solvers/fdmbackwardsolver.hpp>
#include <ql/experimental/finitedifferences/fdmsimple2dextousolver.hpp>
#include <ql/experimental/finitedifferences/fdmexpextouinnervaluecalculator.hpp>
namespace QuantLib {
namespace {
class FdmStorageValue : public FdmInnerValueCalculator {
public:
FdmStorageValue(const boost::shared_ptr<FdmMesher>& mesher)
: mesher_(mesher) { }
Real innerValue(const FdmLinearOpIterator& iter, Time) {
const Real s = std::exp(mesher_->location(iter, 0));
const Real v = mesher_->location(iter, 1);
return s*v;
}
Real avgInnerValue(const FdmLinearOpIterator& iter, Time t) {
return innerValue(iter, t);
}
private:
const boost::shared_ptr<FdmMesher> mesher_;
};
}
FdSimpleExtOUStorageEngine::FdSimpleExtOUStorageEngine(
const boost::shared_ptr<ExtendedOrnsteinUhlenbeckProcess>& process,
const boost::shared_ptr<YieldTermStructure>& rTS,
Size tGrid, Size xGrid,
const FdmSchemeDesc& schemeDesc)
: process_(process),
rTS_ (rTS),
tGrid_(tGrid),
xGrid_(xGrid),
schemeDesc_(schemeDesc) {
}
void FdSimpleExtOUStorageEngine::calculate() const {
QL_REQUIRE(arguments_.exercise->type() == Exercise::Bermudan,
"Bermudan exercise supported only");
// 1. Layout
const Size yGrid = Size(arguments_.capacity/arguments_.changeRate+1);
std::vector<Size> dim;
dim.push_back(xGrid_);
dim.push_back(yGrid);
const boost::shared_ptr<FdmLinearOpLayout> layout(
new FdmLinearOpLayout(dim));
// 2. Mesher
const Time maturity
= rTS_->dayCounter().yearFraction(rTS_->referenceDate(),
arguments_.exercise->lastDate());
const boost::shared_ptr<Fdm1dMesher> xMesher(
new FdmSimpleProcess1dMesher(xGrid_, process_, maturity));
const boost::shared_ptr<Fdm1dMesher> storageMesher(
new Uniform1dMesher(0, arguments_.capacity,
Size(arguments_.capacity/arguments_.changeRate+1)));
std::vector<boost::shared_ptr<Fdm1dMesher> > meshers;
meshers.push_back(xMesher);
meshers.push_back(storageMesher);
boost::shared_ptr<FdmMesher> mesher (
new FdmMesherComposite(layout, meshers));
// 3. Calculator
boost::shared_ptr<FdmInnerValueCalculator> storageCalculator(
new FdmStorageValue(mesher));
// 4. Step conditions
std::list<boost::shared_ptr<StepCondition<Array> > > stepConditions;
std::list<std::vector<Time> > stoppingTimes;
// 4.1 Bermudan step conditions
std::vector<Time> exerciseTimes;
for (Size i=0; i<arguments_.exercise->dates().size(); ++i) {
const Time t = rTS_->dayCounter()
.yearFraction(rTS_->referenceDate(),
arguments_.exercise->dates()[i]);
QL_REQUIRE(t >= 0, "exercise dates must not contain past date");
exerciseTimes.push_back(t);
}
stoppingTimes.push_back(exerciseTimes);
boost::shared_ptr<Payoff> payoff(
new PlainVanillaPayoff(Option::Call, 0.0));
boost::shared_ptr<FdmInnerValueCalculator> underlyingCalculator(
new FdmExpExtOUInnerValueCalculator(payoff, mesher));
stepConditions.push_back(boost::shared_ptr<StepCondition<Array> >(
new FdmSimpleStorageCondition(exerciseTimes,
mesher, underlyingCalculator,
arguments_.changeRate)));
boost::shared_ptr<FdmStepConditionComposite> conditions(
new FdmStepConditionComposite(stoppingTimes, stepConditions));
// 5. Boundary conditions
std::vector<boost::shared_ptr<FdmDirichletBoundary> > boundaries;
// 6. Solver
FdmSolverDesc solverDesc = { mesher, boundaries, conditions,
storageCalculator, maturity, tGrid_, 0 };
boost::shared_ptr<FdmSimple2dExtOUSolver> solver(
new FdmSimple2dExtOUSolver(
Handle<ExtendedOrnsteinUhlenbeckProcess>(process_),
rTS_, solverDesc, schemeDesc_));
const Real x = process_->x0();
const Real y = arguments_.load;
results_.value = solver->valueAt(x, y);
}
}
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