fdsimpleextoustorageengine.cpp

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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
 
/*
 Copyright (C) 2011 Klaus Spanderen
 Copyright (C) 2014 Ralph Schreyer
 
 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 fdsimpleextoustorageengine.cpp
    \brief Finite Differences extended OU engine for simple storage options
*/
 
#include <ql/experimental/finitedifferences/fdmexpextouinnervaluecalculator.hpp>
#include <ql/experimental/finitedifferences/fdmsimple2dextousolver.hpp>
#include <ql/experimental/finitedifferences/fdsimpleextoustorageengine.hpp>
#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>
#include <ql/math/comparison.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/meshers/fdmsimpleprocess1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/predefined1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/uniform1dmesher.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/solvers/fdmbackwardsolver.hpp>
#include <ql/methods/finitedifferences/solvers/fdmsolverdesc.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmsimplestoragecondition.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/pricingengines/vanilla/fdsimplebsswingengine.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <utility>
 
namespace QuantLib {
 
    namespace {
        class FdmStorageValue : public FdmInnerValueCalculator {
          public:
            explicit FdmStorageValue(ext::shared_ptr<FdmMesher> mesher)
            : mesher_(std::move(mesher)) {}
 
            Real innerValue(const FdmLinearOpIterator& iter, Time) override {
                const Real s = std::exp(mesher_->location(iter, 0));
                const Real v = mesher_->location(iter, 1);
                return s*v;
            }
            Real avgInnerValue(const FdmLinearOpIterator& iter, Time t) override {
                return innerValue(iter, t);
            }
 
          private:
            const ext::shared_ptr<FdmMesher> mesher_;
 
        };
 
        class LessButNotCloseEnough {
          public:
            bool operator()(Real a, Real b) const {
                return !(close_enough(a, b, 100) || b < a);
            }
        };
    }
 
    FdSimpleExtOUStorageEngine::FdSimpleExtOUStorageEngine(
        ext::shared_ptr<ExtendedOrnsteinUhlenbeckProcess> process,
        ext::shared_ptr<YieldTermStructure> rTS,
        Size tGrid,
        Size xGrid,
        Size yGrid,
        ext::shared_ptr<Shape> shape,
        const FdmSchemeDesc& schemeDesc)
    : process_(std::move(process)), rTS_(std::move(rTS)), tGrid_(tGrid), xGrid_(xGrid),
      yGrid_(yGrid), shape_(std::move(shape)), schemeDesc_(schemeDesc) {}
 
    void FdSimpleExtOUStorageEngine::calculate() const {
 
        // 1. Exercise
        QL_REQUIRE(arguments_.exercise->type() == Exercise::Bermudan,
                   "Bermudan exercise supported only");
 
        // 2. Mesher
        const Time maturity
            = rTS_->dayCounter().yearFraction(rTS_->referenceDate(),
                                              arguments_.exercise->lastDate());
 
        const ext::shared_ptr<Fdm1dMesher> xMesher(
                     new FdmSimpleProcess1dMesher(xGrid_, process_, maturity));
 
        ext::shared_ptr<Fdm1dMesher> storageMesher;
 
        if(yGrid_ == Null<Size>()){
            //elevator mesher
            std::vector<Real> storageValues(1, arguments_.capacity);
            storageValues.reserve(
                Size(arguments_.capacity/arguments_.changeRate)+1);
 
            for (Real level=0; level <= arguments_.capacity;
                    level+=arguments_.changeRate) {
                    storageValues.push_back(level);
                    storageValues.push_back(arguments_.capacity - level);
            }
 
            const std::set<Real, LessButNotCloseEnough>    orderedValues(
                storageValues.begin(), storageValues.end());
            storageValues.assign(orderedValues.begin(), orderedValues.end());
 
            storageMesher =    ext::shared_ptr<Fdm1dMesher>(
                new Predefined1dMesher(storageValues));
        }
        else {
            // uniform mesher
            storageMesher = ext::shared_ptr<Fdm1dMesher>(
                new Uniform1dMesher(0, arguments_.capacity, yGrid_));
        }
 
        const ext::shared_ptr<FdmMesher> mesher (
            new FdmMesherComposite(xMesher, storageMesher));
 
        // 3. Calculator
        ext::shared_ptr<FdmInnerValueCalculator> storageCalculator(
                                                  new FdmStorageValue(mesher));
 
        // 4. Step conditions
        std::list<ext::shared_ptr<StepCondition<Array> > > stepConditions;
        std::list<std::vector<Time> > stoppingTimes;
 
        // 4.1 Bermudan step conditions
        std::vector<Time> exerciseTimes;
        for (auto i : arguments_.exercise->dates()) {
            const Time t = rTS_->dayCounter().yearFraction(rTS_->referenceDate(), i);
 
            QL_REQUIRE(t >= 0, "exercise dates must not contain past date");
            exerciseTimes.push_back(t);
        }
        stoppingTimes.push_back(exerciseTimes);
 
        ext::shared_ptr<Payoff> payoff(
                                    new PlainVanillaPayoff(Option::Call, 0.0));
 
        ext::shared_ptr<FdmInnerValueCalculator> underlyingCalculator(
            new FdmExpExtOUInnerValueCalculator(payoff, mesher, shape_));
 
        stepConditions.push_back(ext::shared_ptr<StepCondition<Array> >(
            new FdmSimpleStorageCondition(exerciseTimes,
                                          mesher, underlyingCalculator,
                                          arguments_.changeRate)));
 
        ext::shared_ptr<FdmStepConditionComposite> conditions(
                new FdmStepConditionComposite(stoppingTimes, stepConditions));
 
        // 5. Boundary conditions
        const FdmBoundaryConditionSet boundaries;
 
        // 6. Solver
        FdmSolverDesc solverDesc = { mesher, boundaries, conditions,
                                     storageCalculator, maturity, tGrid_, 0 };
 
        ext::shared_ptr<FdmSimple2dExtOUSolver> solver(
                new FdmSimple2dExtOUSolver(
                           Handle<ExtendedOrnsteinUhlenbeckProcess>(process_),
                           rTS_, solverDesc, schemeDesc_));
 
        const Real x = process_->x0();
        const Real y = arguments_.load;
 
        results_.value = solver->valueAt(x, y);
    }
}