fdsabrvanillaengine.cpp

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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
 <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 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_));
    }
}