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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2018 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 fdcevvanillaengine.hpp
\brief Finite-Differences pricing engine for the CEV model
*/
#include <ql/exercise.hpp>
#include <ql/methods/finitedifferences/meshers/concentrating1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmcev1dmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/operators/fdmcevop.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/solvers/fdm1dimsolver.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/utilities/fdmdiscountdirichletboundary.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/methods/finitedifferences/utilities/fdmtimedepdirichletboundary.hpp>
#include <ql/pricingengines/vanilla/analyticcevengine.hpp>
#include <ql/pricingengines/vanilla/fdcevvanillaengine.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <utility>
namespace QuantLib {
namespace {
class PriceAtBoundary {
public:
PriceAtBoundary(Time maturityTime,
ext::shared_ptr<StrikedTypePayoff> payoff,
ext::shared_ptr<YieldTermStructure> rTS,
ext::shared_ptr<CEVCalculator> calculator)
: maturityTime_(maturityTime), payoff_(std::move(payoff)),
calculator_(std::move(calculator)), rTS_(std::move(rTS)) {}
Real operator()(Real t) const {
const Time time2Expiry = std::max(1/365., maturityTime_ - t);
const DiscountFactor df =
rTS_->discount(maturityTime_) / rTS_->discount(t);
return df * calculator_->value(
payoff_->optionType(), payoff_->strike(), time2Expiry);
}
private:
const Time maturityTime_;
const ext::shared_ptr<StrikedTypePayoff> payoff_;
const ext::shared_ptr<CEVCalculator> calculator_;
const ext::shared_ptr<YieldTermStructure> rTS_;
};
}
FdCEVVanillaEngine::FdCEVVanillaEngine(Real f0,
Real alpha,
Real beta,
Handle<YieldTermStructure> discountCurve,
Size tGrid,
Size xGrid,
Size dampingSteps,
Real scalingFactor,
Real eps,
const FdmSchemeDesc& schemeDesc)
: f0_(f0), alpha_(alpha), beta_(beta), discountCurve_(std::move(discountCurve)), tGrid_(tGrid),
xGrid_(xGrid), dampingSteps_(dampingSteps), scalingFactor_(scalingFactor), eps_(eps),
schemeDesc_(schemeDesc) {
registerWith(discountCurve_);
}
void FdCEVVanillaEngine::calculate() const {
// 1. Mesher
const ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-striked payoff given");
const ext::shared_ptr<YieldTermStructure> rTS =
discountCurve_.currentLink();
const DayCounter dc = rTS->dayCounter();
const Date referenceDate = rTS->referenceDate();
const Date maturityDate = arguments_.exercise->lastDate();
const Time maturityTime = dc.yearFraction(referenceDate, maturityDate);
const ext::shared_ptr<Fdm1dMesher> cevMesher =
ext::make_shared<FdmCEV1dMesher>(
xGrid_,
f0_, alpha_, beta_,
maturityTime, eps_, scalingFactor_,
std::make_pair(payoff->strike(), 0.1));
const Real lowerBound = cevMesher->locations().front();
const Real upperBound = cevMesher->locations().back();
const ext::shared_ptr<FdmMesher> mesher =
ext::make_shared<FdmMesherComposite>(cevMesher);
// 2. Calculator
const ext::shared_ptr<FdmInnerValueCalculator> calculator =
ext::make_shared<FdmCellAveragingInnerValue>(payoff, mesher, 0);
// 3. Step conditions
const ext::shared_ptr<FdmStepConditionComposite> conditions =
FdmStepConditionComposite::vanillaComposite(
DividendSchedule(), arguments_.exercise,
mesher, calculator,
referenceDate, dc);
// 4. Boundary conditions
FdmBoundaryConditionSet boundaries;
const PriceAtBoundary upperBoundPrice(
maturityTime, payoff, rTS,
ext::make_shared<CEVCalculator>(upperBound, alpha_, beta_));
boundaries.push_back(ext::make_shared<FdmTimeDepDirichletBoundary>(
mesher, std::function<Real (Real)>(upperBoundPrice),
0, FdmTimeDepDirichletBoundary::Upper));
const Real delta = (1-2*beta_)/(1-beta_);
if (delta < 2.0) {
const Real terminalCashFlow = (*payoff)(lowerBound);
boundaries.push_back(
ext::make_shared<FdmDiscountDirichletBoundary>(
mesher, rTS, maturityTime, terminalCashFlow,
0, FdmTimeDepDirichletBoundary::Lower));
}
// 5. Solver
const FdmSolverDesc solverDesc = {
mesher, boundaries, conditions,
calculator, maturityTime, tGrid_, dampingSteps_
};
const ext::shared_ptr<FdmLinearOpComposite> op =
ext::make_shared<FdmCEVOp>(
mesher, discountCurve_.currentLink(), f0_, alpha_, beta_, 0);
const ext::shared_ptr<Fdm1DimSolver> solver =
ext::make_shared<Fdm1DimSolver>(solverDesc, schemeDesc_, op);
results_.value = solver->interpolateAt(f0_);
results_.delta = solver->derivativeX(f0_);
results_.gamma = solver->derivativeXX(f0_);
results_.theta = solver->thetaAt(f0_);
}
}
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