fdsimpleklugeextouvppengine.cpp

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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 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);
    }
}