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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2019 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 fdsabrvanillaengine.hpp */
#include <ql/exercise.hpp>
#include <ql/math/distributions/normaldistribution.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/fdmsabrop.hpp>
#include <ql/methods/finitedifferences/solvers/fdm2dimsolver.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/utilities/cevrndcalculator.hpp>
#include <ql/methods/finitedifferences/utilities/fdmdiscountdirichletboundary.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/pricingengines/vanilla/fdsabrvanillaengine.hpp>
#include <ql/termstructures/volatility/sabr.hpp>
#include <ql/termstructures/yieldtermstructure.hpp>
#include <utility>
namespace QuantLib {
FdSabrVanillaEngine::FdSabrVanillaEngine(Real f0,
Real alpha,
Real beta,
Real nu,
Real rho,
Handle<YieldTermStructure> rTS,
Size tGrid,
Size fGrid,
Size xGrid,
Size dampingSteps,
Real scalingFactor,
Real eps,
const FdmSchemeDesc& schemeDesc)
: f0_(f0), alpha_(alpha), beta_(beta), nu_(nu), rho_(rho), rTS_(std::move(rTS)), tGrid_(tGrid),
fGrid_(fGrid), xGrid_(xGrid), dampingSteps_(dampingSteps), scalingFactor_(scalingFactor),
eps_(eps), schemeDesc_(schemeDesc) {
validateSabrParameters(alpha, 0.5, nu, rho);
QL_REQUIRE(beta<1.0, "beta must be smaller than 1.0: "
<< beta << " not allowed");
registerWith(rTS_);
}
void FdSabrVanillaEngine::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 DayCounter dc = rTS_->dayCounter();
const Date referenceDate = rTS_->referenceDate();
const Date maturityDate = arguments_.exercise->lastDate();
const Time maturityTime = dc.yearFraction(referenceDate, maturityDate);
const Real upperAlpha = alpha_*
std::exp(nu_*std::sqrt(maturityTime)*InverseCumulativeNormal()(0.75));
const ext::shared_ptr<Fdm1dMesher> cevMesher =
ext::make_shared<FdmCEV1dMesher>(
fGrid_, f0_, upperAlpha, beta_,
maturityTime, eps_, scalingFactor_,
std::make_pair(payoff->strike(), 0.025));
const Real normInvEps = InverseCumulativeNormal()(1-eps_);
const Real logDrift = -0.5*nu_*nu_*maturityTime;
const Real volRange =
nu_*std::sqrt(maturityTime)*normInvEps*scalingFactor_;
const Real xMin = std::log(alpha_) + logDrift - volRange;
const Real xMax = std::log(alpha_) + logDrift + volRange;
const ext::shared_ptr<Fdm1dMesher> xMesher =
ext::make_shared<Concentrating1dMesher>(
xMin, xMax, xGrid_, std::make_pair(std::log(alpha_), 0.1));
const ext::shared_ptr<FdmMesher> mesher =
ext::make_shared<FdmMesherComposite>(cevMesher, xMesher);
// 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 Real lowerBound = cevMesher->locations().front();
const Real upperBound = cevMesher->locations().back();
boundaries.push_back(
ext::make_shared<FdmDiscountDirichletBoundary>(
mesher, rTS_.currentLink(),
maturityTime, (*payoff)(upperBound),
0, FdmDiscountDirichletBoundary::Upper));
boundaries.push_back(
ext::make_shared<FdmDiscountDirichletBoundary>(
mesher, rTS_.currentLink(),
maturityTime, (*payoff)(lowerBound),
0, FdmDiscountDirichletBoundary::Lower));
// 5. Solver
const FdmSolverDesc solverDesc = {
mesher, boundaries, conditions,
calculator, maturityTime, tGrid_, dampingSteps_
};
const ext::shared_ptr<FdmLinearOpComposite> op =
ext::make_shared<FdmSabrOp>(
mesher, rTS_.currentLink(),
f0_, alpha_, beta_, nu_, rho_);
const ext::shared_ptr<Fdm2DimSolver> solver =
ext::make_shared<Fdm2DimSolver>(solverDesc, schemeDesc_, op);
results_.value = solver->interpolateAt(f0_, std::log(alpha_));
}
}
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