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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2008 Frank Hövermann
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/experimental/processes/extendedblackscholesprocess.hpp>
namespace QuantLib {
ExtendedBlackScholesMertonProcess::ExtendedBlackScholesMertonProcess(
const Handle<Quote>& x0,
const Handle<YieldTermStructure>& dividendTS,
const Handle<YieldTermStructure>& riskFreeTS,
const Handle<BlackVolTermStructure>& blackVolTS,
const ext::shared_ptr<discretization>& d,
Discretization evolDisc)
: GeneralizedBlackScholesProcess(x0,dividendTS,riskFreeTS,blackVolTS,d),
discretization_(evolDisc) {}
Real ExtendedBlackScholesMertonProcess::drift(Time t, Real x) const {
Real sigma = diffusion(t,x);
// we could be more anticipatory if we know the right dt
// for which the drift will be used
Time t1 = t + 0.0001;
return riskFreeRate()->forwardRate(t,t1,Continuous,NoFrequency,true).rate()
- dividendYield()->forwardRate(t,t1,Continuous,NoFrequency,true).rate()
- 0.5 * sigma * sigma;
}
Real ExtendedBlackScholesMertonProcess::diffusion(Time t, Real x) const {
return blackVolatility()->blackVol(t, x, true);
}
Real ExtendedBlackScholesMertonProcess::evolve(Time t0, Real x0,
Time dt, Real dw) const {
Real predictor, sigma0, sigma1;
Time t1;
Rate rate0, rate1;
Real driftterm, diffusionterm, corrector;
switch (discretization_) {
case Milstein:
// Milstein scheme
return apply(x0, drift(t0, x0)*dt
+ 0.5*std::pow(diffusion(t0, x0),2)*(dw*dw-1)*dt
+ diffusion(t0,x0)*std::sqrt(dt)*dw);
case Euler:
// Usual Euler scheme
return apply(expectation(t0,x0,dt), stdDeviation(t0,x0,dt)*dw);
case PredictorCorrector:
// Predictor-Corrector scheme with equal weighting
predictor =
apply(expectation(t0,x0,dt), stdDeviation(t0,x0,dt)*dw);
t1 = t0 + 0.0001;
sigma0 = diffusion(t0,x0);
sigma1 = diffusion(t0+dt,predictor);
rate0 =
riskFreeRate()->forwardRate(t0,t1,Continuous,NoFrequency,true).rate()
- dividendYield()->forwardRate(t0,t1,Continuous,NoFrequency,true).rate()
- 0.5*std::pow(sigma0,2);
rate1 =
riskFreeRate()->forwardRate(t0+dt,t1+dt,Continuous,
NoFrequency,true).rate()
- dividendYield()->forwardRate(t0+dt,t1+dt,
Continuous,NoFrequency,true).rate()
- 0.5*std::pow(sigma1,2);
driftterm = 0.5*rate1+0.5*rate0;
diffusionterm = 0.5*(sigma1+sigma0);
corrector =
apply(x0,driftterm*dt+diffusionterm*std::sqrt(dt)*dw);
return corrector;
default:
QL_FAIL("unknown discretization scheme");
}
}
}
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