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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Andreas Gaida
Copyright (C) 2008, 2009 Ralph Schreyer
Copyright (C) 2008, 2009 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.
*/
#include <ql/processes/blackscholesprocess.hpp>
#include <ql/math/interpolations/cubicinterpolation.hpp>
#include <ql/methods/finitedifferences/finitedifferencemodel.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsnapshotcondition.hpp>
#include <ql/methods/finitedifferences/solvers/fdmbackwardsolver.hpp>
#include <ql/methods/finitedifferences/operators/fdmblackscholesop.hpp>
#include <ql/methods/finitedifferences/solvers/fdmblackscholessolver.hpp>
namespace QuantLib {
FdmBlackScholesSolver::FdmBlackScholesSolver(
const Handle<GeneralizedBlackScholesProcess>& process,
Real strike,
const FdmSolverDesc& solverDesc,
const FdmSchemeDesc& schemeDesc,
bool localVol,
Real illegalLocalVolOverwrite)
: process_(process),
strike_(strike),
solverDesc_(solverDesc),
schemeDesc_(schemeDesc),
mesher_(solverDesc.mesher),
thetaCondition_(new FdmSnapshotCondition(
0.99*std::min(1.0/365.0,
solverDesc.condition->stoppingTimes().empty()
? solverDesc.maturity
: solverDesc.condition->stoppingTimes().front()))),
conditions_(FdmStepConditionComposite::joinConditions(thetaCondition_,
solverDesc.condition)),
localVol_(localVol),
illegalLocalVolOverwrite_(illegalLocalVolOverwrite),
initialValues_(mesher_->layout()->size()),
resultValues_(mesher_->layout()->dim()[0]) {
registerWith(process_);
x_.reserve(mesher_->layout()->dim()[0]);
const boost::shared_ptr<FdmLinearOpLayout> layout = mesher_->layout();
const FdmLinearOpIterator endIter = layout->end();
for (FdmLinearOpIterator iter = layout->begin(); iter != endIter;
++iter) {
initialValues_[iter.index()]
= solverDesc.calculator->avgInnerValue(iter,
solverDesc.maturity);
x_.push_back(mesher_->location(iter, 0));
}
}
void FdmBlackScholesSolver::performCalculations() const {
boost::shared_ptr<FdmBlackScholesOp> map(new FdmBlackScholesOp(
mesher_, process_.currentLink(), strike_,
localVol_, illegalLocalVolOverwrite_));
Array rhs(initialValues_.size());
std::copy(initialValues_.begin(), initialValues_.end(), rhs.begin());
FdmBackwardSolver(map, solverDesc_.bcSet, conditions_, schemeDesc_)
.rollback(rhs, solverDesc_.maturity, 0.0,
solverDesc_.timeSteps, solverDesc_.dampingSteps);
std::copy(rhs.begin(), rhs.end(), resultValues_.begin());
interpolation_ = boost::shared_ptr<CubicInterpolation>(new
MonotonicCubicNaturalSpline(x_.begin(), x_.end(),
resultValues_.begin()));
}
Real FdmBlackScholesSolver::valueAt(Real s) const {
calculate();
return interpolation_->operator()(std::log(s));
}
Real FdmBlackScholesSolver::deltaAt(Real s) const {
calculate();
return interpolation_->derivative(std::log(s))/s;
}
Real FdmBlackScholesSolver::gammaAt(Real s) const {
calculate();
return (interpolation_->secondDerivative(std::log(s))
-interpolation_->derivative(std::log(s)))/(s*s);
}
Real FdmBlackScholesSolver::thetaAt(Real s) const {
QL_REQUIRE(conditions_->stoppingTimes().front() > 0.0,
"stopping time at zero-> can't calculate theta");
calculate();
Array thetaValues(resultValues_.size());
const Array& rhs = thetaCondition_->getValues();
std::copy(rhs.begin(), rhs.end(), thetaValues.begin());
Real temp = MonotonicCubicNaturalSpline(
x_.begin(), x_.end(), thetaValues.begin())(std::log(s));
return ( temp - valueAt(s) ) / thetaCondition_->getTime();
}
}
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