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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2009 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
<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.
*/
#include <ql/exercise.hpp>
#include <ql/math/distributions/normaldistribution.hpp>
#include <ql/methods/finitedifferences/meshers/fdmblackscholesmesher.hpp>
#include <ql/methods/finitedifferences/meshers/fdmmeshercomposite.hpp>
#include <ql/methods/finitedifferences/operators/fdmlinearoplayout.hpp>
#include <ql/methods/finitedifferences/solvers/fdmsimple2dbssolver.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmarithmeticaveragecondition.hpp>
#include <ql/methods/finitedifferences/stepconditions/fdmstepconditioncomposite.hpp>
#include <ql/methods/finitedifferences/utilities/fdminnervaluecalculator.hpp>
#include <ql/pricingengines/asian/fdblackscholesasianengine.hpp>
#include <ql/processes/blackscholesprocess.hpp>
#include <utility>
namespace QuantLib {
FdBlackScholesAsianEngine::FdBlackScholesAsianEngine(
ext::shared_ptr<GeneralizedBlackScholesProcess> process,
Size tGrid,
Size xGrid,
Size aGrid,
const FdmSchemeDesc& schemeDesc)
: process_(std::move(process)), tGrid_(tGrid), xGrid_(xGrid), aGrid_(aGrid),
schemeDesc_(schemeDesc) {}
void FdBlackScholesAsianEngine::calculate() const {
QL_REQUIRE(arguments_.exercise->type() == Exercise::European,
"European exercise supported only");
QL_REQUIRE(arguments_.averageType == Average::Arithmetic,
"Arithmetic averaging supported only");
QL_REQUIRE( arguments_.runningAccumulator == 0
|| arguments_.pastFixings > 0,
"Running average requires at least one past fixing");
// 1. Mesher
const ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
const Time maturity = process_->time(arguments_.exercise->lastDate());
const ext::shared_ptr<Fdm1dMesher> equityMesher(
new FdmBlackScholesMesher(xGrid_, process_, maturity,
payoff->strike()));
const Real spot = process_->x0();
QL_REQUIRE(spot > 0.0, "negative or null underlying given");
const Real avg = (arguments_.runningAccumulator == 0)
? spot : arguments_.runningAccumulator/arguments_.pastFixings;
const Real normInvEps = InverseCumulativeNormal()(1-0.0001);
const Real sigmaSqrtT
= process_->blackVolatility()->blackVol(maturity, payoff->strike())
*std::sqrt(maturity);
const Real r = sigmaSqrtT*normInvEps;
Real xMin = std::min(std::log(avg) - 0.25*r, std::log(spot) - 1.5*r);
Real xMax = std::max(std::log(avg) + 0.25*r, std::log(spot) + 1.5*r);
const ext::shared_ptr<Fdm1dMesher> averageMesher(
new FdmBlackScholesMesher(aGrid_, process_, maturity,
payoff->strike(), xMin, xMax));
const ext::shared_ptr<FdmMesher> mesher (
new FdmMesherComposite(equityMesher, averageMesher));
// 2. Calculator
ext::shared_ptr<FdmInnerValueCalculator> calculator(
new FdmLogInnerValue(payoff, mesher, 1));
// 3. Step conditions
std::list<ext::shared_ptr<StepCondition<Array> > > stepConditions;
std::list<std::vector<Time> > stoppingTimes;
// 3.1 Arithmetic average step conditions
std::vector<Time> averageTimes;
for (auto& fixingDate : arguments_.fixingDates) {
Time t = process_->time(fixingDate);
QL_REQUIRE(t >= 0, "Fixing dates must not contain past date");
averageTimes.push_back(t);
}
stoppingTimes.emplace_back(averageTimes);
stepConditions.push_back(ext::shared_ptr<StepCondition<Array> >(
new FdmArithmeticAverageCondition(
averageTimes, arguments_.runningAccumulator,
arguments_.pastFixings, mesher, 0)));
ext::shared_ptr<FdmStepConditionComposite> conditions(
new FdmStepConditionComposite(stoppingTimes, stepConditions));
// 4. Boundary conditions
const FdmBoundaryConditionSet boundaries;
// 5. Solver
FdmSolverDesc solverDesc = { mesher, boundaries, conditions,
calculator, maturity, tGrid_, 0 };
ext::shared_ptr<FdmSimple2dBSSolver> solver(
new FdmSimple2dBSSolver(
Handle<GeneralizedBlackScholesProcess>(process_),
payoff->strike(), solverDesc, schemeDesc_));
results_.value = solver->valueAt(spot, avg);
results_.delta = solver->deltaAt(spot, avg, spot*0.01);
results_.gamma = solver->gammaAt(spot, avg, spot*0.01);
}
}
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