1/* -*- mode: c++; tab-width: 4; indent-tabs-mode: nil; c-basic-offset: 4 -*- */
2
3/*
4 Copyright (C) 2003 Ferdinando Ametrano
5 Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
6 Copyright (C) 2004, 2005 StatPro Italia srl
7
8 This file is part of QuantLib, a free-software/open-source library
9 for financial quantitative analysts and developers - http://quantlib.org/
10
11 QuantLib is free software: you can redistribute it and/or modify it
12 under the terms of the QuantLib license. You should have received a
13 copy of the license along with this program; if not, please email
14 <quantlib-dev@lists.sf.net>. The license is also available online at
15 <http://quantlib.org/license.shtml>.
16
17 This program is distributed in the hope that it will be useful, but WITHOUT
18 ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
19 FOR A PARTICULAR PURPOSE. See the license for more details.
20*/
21
22/*! \file ornsteinuhlenbeckprocess.hpp
23 \brief Ornstein-Uhlenbeck process
24*/
25
26#ifndef quantlib_ornstein_uhlenbeck_process_hpp
27#define quantlib_ornstein_uhlenbeck_process_hpp
28
29#include <ql/stochasticprocess.hpp>
30
31namespace QuantLib {
32
33 //! Ornstein-Uhlenbeck process class
34 /*! This class describes the Ornstein-Uhlenbeck process governed by
35 \f[
36 dx = a (r - x_t) dt + \sigma dW_t.
37 \f]
38
39 \ingroup processes
40 */
41 class OrnsteinUhlenbeckProcess : public StochasticProcess1D {
42 public:
43 OrnsteinUhlenbeckProcess(Real speed,
44 Volatility vol,
45 Real x0 = 0.0,
46 Real level = 0.0);
47 //! \name StochasticProcess interface
48 //@{
49 Real drift(Time t, Real x) const override;
50 Real diffusion(Time t, Real x) const override;
51 Real expectation(Time t0, Real x0, Time dt) const override;
52 Real stdDeviation(Time t0, Real x0, Time dt) const override;
53 //@}
54 Real x0() const override;
55 Real speed() const;
56 Real volatility() const;
57 Real level() const;
58 Real variance(Time t0, Real x0, Time dt) const override;
59
60 private:
61 Real x0_, speed_, level_;
62 Volatility volatility_;
63 };
64
65 // inline
66
67 inline Real OrnsteinUhlenbeckProcess::x0() const {
68 return x0_;
69 }
70
71 inline Real OrnsteinUhlenbeckProcess::speed() const {
72 return speed_;
73 }
74
75 inline Real OrnsteinUhlenbeckProcess::volatility() const {
76 return volatility_;
77 }
78
79 inline Real OrnsteinUhlenbeckProcess::level() const {
80 return level_;
81 }
82
83 inline Real OrnsteinUhlenbeckProcess::drift(Time, Real x) const {
84 return speed_ * (level_ - x);
85 }
86
87 inline Real OrnsteinUhlenbeckProcess::diffusion(Time, Real) const {
88 return volatility_;
89 }
90
91 inline Real OrnsteinUhlenbeckProcess::expectation(Time, Real x0,
92 Time dt) const {
93 return level_ + (x0 - level_) * std::exp(x: -speed_*dt);
94 }
95
96 inline Real OrnsteinUhlenbeckProcess::stdDeviation(Time t, Real x0,
97 Time dt) const {
98 return std::sqrt(x: variance(t0: t,x0,dt));
99 }
100
101}
102
103#endif
104

source code of quantlib/ql/processes/ornsteinuhlenbeckprocess.hpp