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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2004 Ferdinando Ametrano
Copyright (C) 2007 StatPro Italia srl
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.
*/
#include <ql/pricingengines/vanilla/jumpdiffusionengine.hpp>
#include <ql/pricingengines/vanilla/analyticeuropeanengine.hpp>
#include <ql/math/distributions/poissondistribution.hpp>
#include <ql/termstructures/yield/flatforward.hpp>
#include <ql/termstructures/volatility/equityfx/blackconstantvol.hpp>
#include <ql/utilities/dataformatters.hpp>
#include <ql/exercise.hpp>
namespace QuantLib {
JumpDiffusionEngine::JumpDiffusionEngine(
const boost::shared_ptr<Merton76Process>& process,
Real relativeAccuracy,
Size maxIterations)
: process_(process), relativeAccuracy_(relativeAccuracy),
maxIterations_(maxIterations) {
registerWith(process_);
}
void JumpDiffusionEngine::calculate() const {
Real jumpSquareVol = process_->logJumpVolatility()->value()
* process_->logJumpVolatility()->value();
Real muPlusHalfSquareVol = process_->logMeanJump()->value()
+ 0.5*jumpSquareVol;
// mean jump size
Real k = std::exp(muPlusHalfSquareVol) - 1.0;
Real lambda = (k+1.0) * process_->jumpIntensity()->value();
boost::shared_ptr<StrikedTypePayoff> payoff =
boost::dynamic_pointer_cast<StrikedTypePayoff>(arguments_.payoff);
QL_REQUIRE(payoff, "non-striked payoff given");
Real variance =
process_->blackVolatility()->blackVariance(
arguments_.exercise->lastDate(),
payoff->strike());
DayCounter voldc = process_->blackVolatility()->dayCounter();
Calendar volcal = process_->blackVolatility()->calendar();
Date volRefDate = process_->blackVolatility()->referenceDate();
Time t = voldc.yearFraction(volRefDate,
arguments_.exercise->lastDate());
Rate riskFreeRate = -std::log(process_->riskFreeRate()->discount(
arguments_.exercise->lastDate()))/t;
Date rateRefDate = process_->riskFreeRate()->referenceDate();
PoissonDistribution p(lambda*t);
Handle<Quote> stateVariable = process_->stateVariable();
Handle<YieldTermStructure> dividendTS = process_->dividendYield();
RelinkableHandle<YieldTermStructure> riskFreeTS(
*process_->riskFreeRate());
RelinkableHandle<BlackVolTermStructure> volTS(
*process_->blackVolatility());
boost::shared_ptr<GeneralizedBlackScholesProcess> bsProcess(
new GeneralizedBlackScholesProcess(stateVariable, dividendTS,
riskFreeTS, volTS));
AnalyticEuropeanEngine baseEngine(bsProcess);
VanillaOption::arguments* baseArguments =
dynamic_cast<VanillaOption::arguments*>(baseEngine.getArguments());
baseArguments->payoff = arguments_.payoff;
baseArguments->exercise = arguments_.exercise;
baseArguments->validate();
const VanillaOption::results* baseResults =
dynamic_cast<const VanillaOption::results*>(
baseEngine.getResults());
results_.value = 0.0;
results_.delta = 0.0;
results_.gamma = 0.0;
results_.theta = 0.0;
results_.vega = 0.0;
results_.rho = 0.0;
results_.dividendRho = 0.0;
Real r, v, weight, lastContribution = 1.0;
Size i;
Real theta_correction;
// Haug arbitrary criterium is:
//for (i=0; i<11; i++) {
for (i=0; (lastContribution>relativeAccuracy_ && i<maxIterations_)
|| i < Size(lambda*t); i++) {
// constant vol/rate assumption. It should be relaxed
v = std::sqrt((variance + i*jumpSquareVol)/t);
r = riskFreeRate - process_->jumpIntensity()->value()*k
+ i*muPlusHalfSquareVol/t;
riskFreeTS.linkTo(boost::shared_ptr<YieldTermStructure>(new
FlatForward(rateRefDate, r, voldc)));
volTS.linkTo(boost::shared_ptr<BlackVolTermStructure>(new
BlackConstantVol(rateRefDate, volcal, v, voldc)));
baseArguments->validate();
baseEngine.calculate();
weight = p(Size(i));
results_.value += weight * baseResults->value;
results_.delta += weight * baseResults->delta;
results_.gamma += weight * baseResults->gamma;
results_.vega += weight * (std::sqrt(variance/t)/v)*
baseResults->vega;
// theta modified
theta_correction = baseResults->vega*((i*jumpSquareVol)/
(2.0*v*t*t)) +
baseResults->rho*i*muPlusHalfSquareVol/(t*t);
results_.theta += weight *(baseResults->theta + theta_correction +
lambda*baseResults->value);
if(i != 0){
results_.theta -= (p(Size(i-1))*lambda* baseResults->value);
}
//end theta calculation
results_.rho += weight * baseResults->rho;
results_.dividendRho += weight * baseResults->dividendRho;
lastContribution = std::fabs(baseResults->value /
(std::fabs(results_.value)>QL_EPSILON ? results_.value : 1.0));
lastContribution = std::max<Real>(lastContribution,
std::fabs(baseResults->delta /
(std::fabs(results_.delta)>QL_EPSILON ? results_.delta : 1.0)));
lastContribution = std::max<Real>(lastContribution,
std::fabs(baseResults->gamma /
(std::fabs(results_.gamma)>QL_EPSILON ? results_.gamma : 1.0)));
lastContribution = std::max<Real>(lastContribution,
std::fabs(baseResults->theta /
(std::fabs(results_.theta)>QL_EPSILON ? results_.theta : 1.0)));
lastContribution = std::max<Real>(lastContribution,
std::fabs(baseResults->vega /
(std::fabs(results_.vega)>QL_EPSILON ? results_.vega : 1.0)));
lastContribution = std::max<Real>(lastContribution,
std::fabs(baseResults->rho /
(std::fabs(results_.rho)>QL_EPSILON ? results_.rho : 1.0)));
lastContribution = std::max<Real>(lastContribution,
std::fabs(baseResults->dividendRho /
(std::fabs(results_.dividendRho)>QL_EPSILON ?
results_.dividendRho : 1.0)));
lastContribution *= weight;
}
QL_ENSURE(i<maxIterations_,
i << " iterations have been not enough to reach "
<< "the required " << relativeAccuracy_
<< " accuracy. The " << io::ordinal(i)
<< " addendum was " << lastContribution
<< " while the running sum was " << results_.value);
}
}
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