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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/pricingengines/barrier/fdhestonrebateengine.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/solvers/fdmbackwardsolver.hpp>
#include <ql/methods/finitedifferences/meshers/fdmhestonvariancemesher.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/meshers/fdmblackscholesmesher.hpp>
namespace QuantLib {
FdHestonRebateEngine::FdHestonRebateEngine(
const boost::shared_ptr<HestonModel>& model,
Size tGrid, Size xGrid, Size vGrid, Size dampingSteps,
const FdmSchemeDesc& schemeDesc)
: GenericModelEngine<HestonModel,
DividendBarrierOption::arguments,
DividendBarrierOption::results>(model),
tGrid_(tGrid), xGrid_(xGrid), vGrid_(vGrid),
dampingSteps_(dampingSteps),
schemeDesc_(schemeDesc) {
}
void FdHestonRebateEngine::calculate() const {
// 1. Layout
std::vector<Size> dim;
dim.push_back(xGrid_);
dim.push_back(vGrid_);
boost::shared_ptr<FdmLinearOpLayout> layout(new FdmLinearOpLayout(dim));
// 2. Mesher
const boost::shared_ptr<HestonProcess>& process = model_->process();
const Time maturity = process->time(arguments_.exercise->lastDate());
// 2.1 The variance mesher
const Size tGridMin = 5;
const boost::shared_ptr<FdmHestonVarianceMesher> varianceMesher(
new FdmHestonVarianceMesher(layout->dim()[1], process, maturity,
std::max(tGridMin, tGrid_/50)));
// 2.2 The equity mesher
const boost::shared_ptr<StrikedTypePayoff> payoff =
boost::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
Real xMin=Null<Real>();
Real xMax=Null<Real>();
if ( arguments_.barrierType == Barrier::DownIn
|| arguments_.barrierType == Barrier::DownOut) {
xMin = std::log(arguments_.barrier);
}
if ( arguments_.barrierType == Barrier::UpIn
|| arguments_.barrierType == Barrier::UpOut) {
xMax = std::log(arguments_.barrier);
}
const boost::shared_ptr<Fdm1dMesher> equityMesher(
new FdmBlackScholesMesher(
xGrid_,
FdmBlackScholesMesher::processHelper(
process->s0(), process->dividendYield(),
process->riskFreeRate(), varianceMesher->volaEstimate()),
maturity, payoff->strike(), xMin, xMax));
std::vector<boost::shared_ptr<Fdm1dMesher> > meshers;
meshers.push_back(equityMesher);
meshers.push_back(varianceMesher);
const boost::shared_ptr<FdmMesher> mesher (
new FdmMesherComposite(layout, meshers));
// 3. Calculator
const boost::shared_ptr<StrikedTypePayoff> rebatePayoff(
new CashOrNothingPayoff(Option::Call, 0.0, arguments_.rebate));
const boost::shared_ptr<FdmInnerValueCalculator> calculator(
new FdmLogInnerValue(rebatePayoff, mesher, 0));
// 4. Step conditions
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"only european style option are supported");
const boost::shared_ptr<FdmStepConditionComposite> conditions =
FdmStepConditionComposite::vanillaComposite(
arguments_.cashFlow, arguments_.exercise,
mesher, calculator,
process->riskFreeRate()->referenceDate(),
process->riskFreeRate()->dayCounter());
// 5. Boundary conditions
std::vector<boost::shared_ptr<FdmDirichletBoundary> > boundaries;
if ( arguments_.barrierType == Barrier::DownIn
|| arguments_.barrierType == Barrier::DownOut) {
boundaries.push_back(boost::shared_ptr<FdmDirichletBoundary>(
new FdmDirichletBoundary(mesher, arguments_.rebate, 0,
FdmDirichletBoundary::Lower)));
}
if ( arguments_.barrierType == Barrier::UpIn
|| arguments_.barrierType == Barrier::UpOut) {
boundaries.push_back(boost::shared_ptr<FdmDirichletBoundary>(
new FdmDirichletBoundary(mesher, arguments_.rebate, 0,
FdmDirichletBoundary::Upper)));
}
// 6. Solver
FdmSolverDesc solverDesc = { mesher, boundaries, conditions,
calculator, maturity,
tGrid_, dampingSteps_ };
boost::shared_ptr<FdmHestonSolver> solver(new FdmHestonSolver(
Handle<HestonProcess>(process), solverDesc, schemeDesc_));
const Real spot = process->s0()->value();
results_.value = solver->valueAt(spot, process->v0());
results_.delta = solver->deltaAt(spot, process->v0());
results_.gamma = solver->gammaAt(spot, process->v0());
results_.theta = solver->thetaAt(spot, process->v0());
}
}
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