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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2007 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 analyticbsmhullwhiteengine.hpp
\brief analytic Black-Scholes engines including stochastic interest rates
*/
#include <ql/pricingengines/vanilla/analyticbsmhullwhiteengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/termstructures/volatility/equityfx/blackvoltermstructure.hpp>
#include <utility>
namespace QuantLib {
namespace {
class ShiftedBlackVolTermStructure : public BlackVolTermStructure {
public:
ShiftedBlackVolTermStructure(
Real varianceOffset,
const Handle<BlackVolTermStructure> & volTS)
: BlackVolTermStructure(volTS->referenceDate(),
volTS->calendar(),
Following,
volTS->dayCounter()),
varianceOffset_(varianceOffset),
volTS_(volTS) { }
Real minStrike() const override { return volTS_->minStrike(); }
Real maxStrike() const override { return volTS_->maxStrike(); }
Date maxDate() const override { return volTS_->maxDate(); }
protected:
Real blackVarianceImpl(Time t, Real strike) const override {
return volTS_->blackVariance(t, strike, true)+varianceOffset_;
}
Volatility blackVolImpl(Time t, Real strike) const override {
Time nonZeroMaturity = (t==0.0 ? 0.00001 : t);
Real var = blackVarianceImpl(nonZeroMaturity, strike);
return std::sqrt(var/nonZeroMaturity);
}
private:
const Real varianceOffset_;
const Handle<BlackVolTermStructure> volTS_;
};
}
AnalyticBSMHullWhiteEngine::AnalyticBSMHullWhiteEngine(
Real equityShortRateCorrelation,
ext::shared_ptr<GeneralizedBlackScholesProcess> process,
const ext::shared_ptr<HullWhite>& model)
: GenericModelEngine<HullWhite, VanillaOption::arguments, VanillaOption::results>(model),
rho_(equityShortRateCorrelation), process_(std::move(process)) {
QL_REQUIRE(process_, "no Black-Scholes process specified");
QL_REQUIRE(!model_.empty(), "no Hull-White model specified");
registerWith(process_);
}
void AnalyticBSMHullWhiteEngine::calculate() const {
QL_REQUIRE(process_->x0() > 0.0, "negative or null underlying given");
const ext::shared_ptr<StrikedTypePayoff> payoff =
ext::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-striked payoff given");
const ext::shared_ptr<Exercise> exercise = arguments_.exercise;
Time t = process_->riskFreeRate()->dayCounter().yearFraction(
process_->riskFreeRate()->referenceDate(),
exercise->lastDate());
const Real a = model_->params()[0];
const Real sigma = model_->params()[1];
const Real eta =
process_->blackVolatility()->blackVol(exercise->lastDate(),
payoff->strike());
Real varianceOffset;
if (a*t > std::pow(QL_EPSILON, 0.25)) {
const Real v = sigma*sigma/(a*a)
*(t + 2/a*std::exp(-a*t) - 1/(2*a)*std::exp(-2*a*t) - 3/(2*a));
const Real mu = 2*rho_*sigma*eta/a*(t-1/a*(1-std::exp(-a*t)));
varianceOffset = v + mu;
}
else {
// low-a algebraic limit
const Real v = sigma*sigma*t*t*t*(1/3.0-0.25*a*t+7/60.0*a*a*t*t);
const Real mu = rho_*sigma*eta*t*t*(1-a*t/3.0+a*a*t*t/12.0);
varianceOffset = v + mu;
}
Handle<BlackVolTermStructure> volTS(
ext::shared_ptr<BlackVolTermStructure>(
new ShiftedBlackVolTermStructure(varianceOffset,
process_->blackVolatility())));
ext::shared_ptr<GeneralizedBlackScholesProcess> adjProcess(
new GeneralizedBlackScholesProcess(process_->stateVariable(),
process_->dividendYield(),
process_->riskFreeRate(),
volTS));
ext::shared_ptr<AnalyticEuropeanEngine> bsmEngine(
new AnalyticEuropeanEngine(adjProcess));
VanillaOption(payoff, exercise).setupArguments(
bsmEngine->getArguments());
bsmEngine->calculate();
results_ = *dynamic_cast<const OneAssetOption::results*>(
bsmEngine->getResults());
}
}
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