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/*
Copyright (C) 2001, 2002 Sadruddin Rejeb
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 ferdinando@ametrano.net
The license is also available online at http://quantlib.org/html/license.html
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 diffusionprocess.hpp
\brief Diffusion process
\fullpath
ql/%diffusionprocess.hpp
*/
// $Id: diffusionprocess.hpp,v 1.9 2002/03/06 07:16:06 sadrejeb Exp $
#ifndef quantlib_diffusion_process_h
#define quantlib_diffusion_process_h
#include <ql/qldefines.hpp>
#include <ql/types.hpp>
namespace QuantLib {
//! Diffusion process class
/*! This class describes a stochastic process goverved by
\f[
dx = \mu(t, x)dt + \sigma(t, x)dW_t
\f].
*/
class DiffusionProcess {
public:
DiffusionProcess(double x0) : x0_(x0) {}
virtual ~DiffusionProcess() {}
double x0() const { return x0_; }
virtual double drift(Time t, double x) const = 0;
virtual double diffusion(Time t, double x) const = 0;
//! Euler approximation of the expectation
virtual double expectation(Time t0, double x0, Time dt) const {
return x0 + drift(t0, x0)*dt;
}
//! Euler approximation of the variance
virtual double variance(Time t0, double x0, Time dt) const {
double sigma = diffusion(t0, x0);
return sigma*sigma*dt;
}
private:
double x0_;
};
//! Black-Scholes diffusion process class
/*! This class describes the stochastic process governed by
\f[
dS = r dt + \sigma dW_t
\f].
*/
class BlackScholesProcess : public DiffusionProcess {
public:
BlackScholesProcess(Rate rate, double volatility, double s0 = 0.0)
: DiffusionProcess(s0), r_(rate), sigma_(volatility) {}
virtual double drift(Time t, double x) const {
return - r_*x;
}
virtual double diffusion(Time t, double x) const {
return sigma_;
}
virtual double expectation(Time t0, double x0, Time dt) const {
return x0 + r_*dt;
}
virtual double variance(Time t0, double x0, Time dt) const {
return sigma_*sigma_*dt;
}
private:
double r_, sigma_;
};
//! Ornstein-Uhlenbeck process class
/*! This class describes the Ornstein-Uhlenbeck process governed by
\f[
dx = -a x dt + \sigma dW_t
\f].
*/
class OrnsteinUhlenbeckProcess : public DiffusionProcess {
public:
OrnsteinUhlenbeckProcess(double speed, double vol, double x0 = 0.0)
: DiffusionProcess(x0), speed_(speed), volatility_(vol) {}
virtual double drift(Time t, double x) const {
return - speed_*x;
}
virtual double diffusion(Time t, double x) const {
return volatility_;
}
virtual double expectation(Time t0, double x0, Time dt) const {
return x0*QL_EXP(-speed_*dt);
}
virtual double variance(Time t0, double x0, Time dt) const {
return 0.5*volatility_*volatility_/speed_*
(1.0 - QL_EXP(-2.0*speed_*dt));
}
private:
double speed_, volatility_;
};
}
#endif
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