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/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
/*
Copyright (C) 2003 Ferdinando Ametrano
Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
Copyright (C) 2004, 2005 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.
*/
/*! \file ornsteinuhlenbeckprocess.hpp
\brief Ornstein-Uhlenbeck process
*/
#ifndef quantlib_ornstein_uhlenbeck_process_hpp
#define quantlib_ornstein_uhlenbeck_process_hpp
#include <ql/stochasticprocess.hpp>
namespace QuantLib {
//! Ornstein-Uhlenbeck process class
/*! This class describes the Ornstein-Uhlenbeck process governed by
\f[
dx = a (r - x_t) dt + \sigma dW_t.
\f]
\ingroup processes
*/
class OrnsteinUhlenbeckProcess : public StochasticProcess1D {
public:
OrnsteinUhlenbeckProcess(Real speed,
Volatility vol,
Real x0 = 0.0,
Real level = 0.0);
//! \name StochasticProcess interface
//@{
Real drift(Time t,
Real x) const;
Real diffusion(Time t,
Real x) const;
Real expectation(Time t0,
Real x0,
Time dt) const;
Real stdDeviation(Time t0,
Real x0,
Time dt) const;
//@}
Real x0() const;
Real speed() const;
Real volatility() const;
Real level() const;
Real variance(Time t0,
Real x0,
Time dt) const;
private:
Real x0_, speed_, level_;
Volatility volatility_;
};
// inline
inline Real OrnsteinUhlenbeckProcess::x0() const {
return x0_;
}
inline Real OrnsteinUhlenbeckProcess::speed() const {
return speed_;
}
inline Real OrnsteinUhlenbeckProcess::volatility() const {
return volatility_;
}
inline Real OrnsteinUhlenbeckProcess::level() const {
return level_;
}
inline Real OrnsteinUhlenbeckProcess::drift(Time, Real x) const {
return speed_ * (level_ - x);
}
inline Real OrnsteinUhlenbeckProcess::diffusion(Time, Real) const {
return volatility_;
}
inline Real OrnsteinUhlenbeckProcess::expectation(Time, Real x0,
Time dt) const {
return level_ + (x0 - level_) * std::exp(-speed_*dt);
}
inline Real OrnsteinUhlenbeckProcess::stdDeviation(Time t, Real x0,
Time dt) const {
return std::sqrt(variance(t,x0,dt));
}
}
#endif
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