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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
<https://www.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 fdsimpleklugeouvppengine.cpp
\brief Finite Differences engine for simple vpp options
*/
#include <ql/experimental/finitedifferences/fdmexpextouinnervaluecalculator.hpp>
#include <ql/experimental/finitedifferences/fdmklugeextousolver.hpp>
#include <ql/experimental/finitedifferences/fdmvppstepconditionfactory.hpp>
#include <ql/experimental/finitedifferences/fdsimpleklugeextouvppengine.hpp>
#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>
#include <ql/experimental/processes/extouwithjumpsprocess.hpp>
#include <ql/experimental/processes/klugeextouprocess.hpp>
#include <ql/instruments/basketoption.hpp>
#include <ql/instruments/vanillaswingoption.hpp>
#include <ql/methods/finitedifferences/meshers/exponentialjump1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdm1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/meshers/fdmsimpleprocess1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/solvers/fdmsolverdesc.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <list>
#include <utility>
namespace QuantLib {
namespace {
class FdmSparkSpreadInnerValue : public FdmInnerValueCalculator {
public:
FdmSparkSpreadInnerValue(ext::shared_ptr<BasketPayoff> basketPayoff,
ext::shared_ptr<FdmInnerValueCalculator> fuelPrice,
ext::shared_ptr<FdmInnerValueCalculator> powerPrice)
: basketPayoff_(std::move(basketPayoff)), fuelPrice_(std::move(fuelPrice)),
powerPrice_(std::move(powerPrice)) {}
Real innerValue(const FdmLinearOpIterator& iter, Time t) override {
Array s(2);
s[0] = powerPrice_->innerValue(iter, t);
s[1] = fuelPrice_->innerValue(iter, t);
return (*basketPayoff_)(s);
}
Real avgInnerValue(const FdmLinearOpIterator& iter, Time t) override {
return innerValue(iter, t);
}
private:
const ext::shared_ptr<BasketPayoff> basketPayoff_;
const ext::shared_ptr<FdmInnerValueCalculator> fuelPrice_;
const ext::shared_ptr<FdmInnerValueCalculator> powerPrice_;
};
}
FdSimpleKlugeExtOUVPPEngine::FdSimpleKlugeExtOUVPPEngine(
ext::shared_ptr<KlugeExtOUProcess> process,
ext::shared_ptr<YieldTermStructure> rTS,
ext::shared_ptr<Shape> fuelShape,
ext::shared_ptr<Shape> powerShape,
Real fuelCostAddon,
Size tGrid,
Size xGrid,
Size yGrid,
Size gGrid,
const FdmSchemeDesc& schemeDesc)
: process_(std::move(process)), rTS_(std::move(rTS)), fuelCostAddon_(fuelCostAddon),
fuelShape_(std::move(fuelShape)), powerShape_(std::move(powerShape)), tGrid_(tGrid),
xGrid_(xGrid), yGrid_(yGrid), gGrid_(gGrid), schemeDesc_(schemeDesc) {}
void FdSimpleKlugeExtOUVPPEngine::calculate() const {
ext::shared_ptr<SwingExercise> swingExercise(
ext::dynamic_pointer_cast<SwingExercise>(arguments_.exercise));
QL_REQUIRE(swingExercise, "Swing exercise supported only");
const FdmVPPStepConditionFactory stepConditionFactory(arguments_);
// 1. Exercise definition
const std::vector<Time> exerciseTimes
= swingExercise->exerciseTimes(rTS_->dayCounter(),
rTS_->referenceDate());
// 2. mesher set-up
const Time maturity = exerciseTimes.back();
const ext::shared_ptr<ExtOUWithJumpsProcess> klugeProcess
= process_->getKlugeProcess();
const ext::shared_ptr<StochasticProcess1D> klugeOUProcess
= klugeProcess->getExtendedOrnsteinUhlenbeckProcess();
const ext::shared_ptr<Fdm1dMesher> xMesher(
new FdmSimpleProcess1dMesher(xGrid_, klugeOUProcess, maturity));
const ext::shared_ptr<Fdm1dMesher> yMesher(
new ExponentialJump1dMesher(yGrid_,
klugeProcess->beta(),
klugeProcess->jumpIntensity(),
klugeProcess->eta(), 1e-3));
const ext::shared_ptr<Fdm1dMesher> gMesher(
new FdmSimpleProcess1dMesher(gGrid_,
process_->getExtOUProcess(),maturity));
const ext::shared_ptr<Fdm1dMesher> exerciseMesher(
stepConditionFactory.stateMesher());
const ext::shared_ptr<FdmMesher> mesher (
new FdmMesherComposite(xMesher, yMesher, gMesher, exerciseMesher));
// 3. Calculator
const ext::shared_ptr<FdmInnerValueCalculator> zeroInnerValue(
new FdmZeroInnerValue());
const ext::shared_ptr<Payoff> zeroStrikeCall(
new PlainVanillaPayoff(Option::Call, 0.0));
const ext::shared_ptr<FdmInnerValueCalculator> fuelPrice(
new FdmExpExtOUInnerValueCalculator(zeroStrikeCall,
mesher, fuelShape_, 2));
const ext::shared_ptr<FdmInnerValueCalculator> powerPrice(
new FdmExtOUJumpModelInnerValue(zeroStrikeCall,mesher,powerShape_));
const ext::shared_ptr<FdmInnerValueCalculator> sparkSpread(
new FdmSparkSpreadInnerValue(
ext::dynamic_pointer_cast<BasketPayoff>(arguments_.payoff),
fuelPrice, powerPrice));
// 4. Step conditions
std::list<std::vector<Time> > stoppingTimes;
std::list<ext::shared_ptr<StepCondition<Array> > > stepConditions;
// 4.1 Bermudan step conditions
stoppingTimes.push_back(exerciseTimes);
const FdmVPPStepConditionMesher mesh = {3U, mesher};
const ext::shared_ptr<FdmVPPStepCondition> stepCondition(
stepConditionFactory.build(mesh, fuelCostAddon_,
fuelPrice, sparkSpread));
stepConditions.push_back(stepCondition);
const ext::shared_ptr<FdmStepConditionComposite> conditions(
new FdmStepConditionComposite(stoppingTimes, stepConditions));
// 5. Boundary conditions
const FdmBoundaryConditionSet boundaries;
// 6. set-up solver
FdmSolverDesc solverDesc = { mesher, boundaries, conditions,
zeroInnerValue, maturity, tGrid_, 0 };
const ext::shared_ptr<FdmKlugeExtOUSolver<4> > solver(
new FdmKlugeExtOUSolver<4>(Handle<KlugeExtOUProcess>(process_),
rTS_, solverDesc, schemeDesc_));
std::vector<Real> x(4);
x[0] = process_->initialValues()[0];
x[1] = process_->initialValues()[1];
x[2] = process_->initialValues()[2];
const Real tol = 1e-8;
const Real maxExerciseValue = exerciseMesher->locations().back();
const Real minExerciseValue = exerciseMesher->locations().front();
Array results(exerciseMesher->size());
for (Size i=0; i < results.size(); ++i) {
x[3] = std::max(minExerciseValue + tol,
std::min(exerciseMesher->location(i),
maxExerciseValue - tol));
results[i] = solver->valueAt(x);
}
results_.value = stepCondition->maxValue(results);
}
}
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