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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 fdsimplebsswingengine.cpp
\brief Finite Differences Black-Scholes engine for simple swing options
*/
#include <ql/processes/blackscholesprocess.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/fdmblackscholesmesher.hpp>
#include <ql/pricingengines/vanilla/fdsimplebsswingengine.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsimpleswingcondition.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/solvers/fdmsimple2dbssolver.hpp>
namespace QuantLib {
FdSimpleBSSwingEngine::FdSimpleBSSwingEngine(
const boost::shared_ptr<GeneralizedBlackScholesProcess>& process,
Size tGrid, Size xGrid,
const FdmSchemeDesc& schemeDesc)
: process_(process),
tGrid_(tGrid),
xGrid_(xGrid),
schemeDesc_(schemeDesc) {
}
void FdSimpleBSSwingEngine::calculate() const {
QL_REQUIRE(arguments_.exercise->type() == Exercise::Bermudan,
"Bermudan exercise supported only");
// 1. Layout
std::vector<Size> dim;
dim.push_back(xGrid_);
dim.push_back(arguments_.maxExerciseRights+1);
const boost::shared_ptr<FdmLinearOpLayout> layout(
new FdmLinearOpLayout(dim));
// 2. Mesher
const boost::shared_ptr<StrikedTypePayoff> payoff =
boost::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
const Time maturity = process_->time(arguments_.exercise->lastDate());
const boost::shared_ptr<Fdm1dMesher> equityMesher(
new FdmBlackScholesMesher(xGrid_, process_,
maturity, payoff->strike()));
const boost::shared_ptr<Fdm1dMesher> exerciseMesher(
new Uniform1dMesher(0, arguments_.maxExerciseRights,
arguments_.maxExerciseRights+1));
std::vector<boost::shared_ptr<Fdm1dMesher> > meshers;
meshers.push_back(equityMesher);
meshers.push_back(exerciseMesher);
boost::shared_ptr<FdmMesher> mesher (
new FdmMesherComposite(layout, meshers));
// 3. Calculator
boost::shared_ptr<FdmInnerValueCalculator> calculator(
new FdmZeroInnerValue());
// 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) {
Time t = process_->time(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<FdmInnerValueCalculator> exerciseCalculator(
new FdmLogInnerValue(payoff, mesher, 0));
stepConditions.push_back(boost::shared_ptr<StepCondition<Array> >(
new FdmSimpleSwingCondition(exerciseTimes, mesher,
exerciseCalculator, 1)));
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,
calculator, maturity, tGrid_, 0 };
boost::shared_ptr<FdmSimple2dBSSolver> solver(
new FdmSimple2dBSSolver(
Handle<GeneralizedBlackScholesProcess>(process_),
payoff->strike(), solverDesc, schemeDesc_));
const Real spot = process_->x0();
std::vector< std::pair<Real, Real> > exerciseValues;
for (Size i=arguments_.minExerciseRights;
i <= arguments_.maxExerciseRights; ++i) {
const Real y = std::exp(Real(i));
exerciseValues.push_back(
std::pair<Real, Real>(solver->valueAt(spot, y), y));
}
const Real y = std::max_element(exerciseValues.begin(),
exerciseValues.end())->second;
results_.value = solver->valueAt(spot, y);
results_.delta = solver->deltaAt(spot, y, spot*0.01);
results_.gamma = solver->gammaAt(spot, y, spot*0.01);
results_.theta = solver->thetaAt(spot, y);
}
}
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