/usr/include/ql/stochasticprocess.hpp is in libquantlib0-dev 1.7.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 | /* -*- 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 stochasticprocess.hpp
\brief stochastic processes
*/
#ifndef quantlib_stochastic_process_hpp
#define quantlib_stochastic_process_hpp
#include <ql/time/date.hpp>
#include <ql/patterns/observable.hpp>
#include <ql/math/matrix.hpp>
namespace QuantLib {
//! multi-dimensional stochastic process class.
/*! This class describes a stochastic process governed by
\f[
d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t
+ \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t.
\f]
*/
class StochasticProcess : public Observer, public Observable {
public:
//! discretization of a stochastic process over a given time interval
class discretization {
public:
virtual ~discretization() {}
virtual Disposable<Array> drift(const StochasticProcess&,
Time t0, const Array& x0,
Time dt) const = 0;
virtual Disposable<Matrix> diffusion(
const StochasticProcess&,
Time t0, const Array& x0,
Time dt) const = 0;
virtual Disposable<Matrix> covariance(
const StochasticProcess&,
Time t0, const Array& x0,
Time dt) const = 0;
};
virtual ~StochasticProcess() {}
//! \name Stochastic process interface
//@{
//! returns the number of dimensions of the stochastic process
virtual Size size() const = 0;
//! returns the number of independent factors of the process
virtual Size factors() const;
//! returns the initial values of the state variables
virtual Disposable<Array> initialValues() const = 0;
/*! \brief returns the drift part of the equation, i.e.,
\f$ \mu(t, \mathrm{x}_t) \f$
*/
virtual Disposable<Array> drift(Time t,
const Array& x) const = 0;
/*! \brief returns the diffusion part of the equation, i.e.
\f$ \sigma(t, \mathrm{x}_t) \f$
*/
virtual Disposable<Matrix> diffusion(Time t,
const Array& x) const = 0;
/*! returns the expectation
\f$ E(\mathrm{x}_{t_0 + \Delta t}
| \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
of the process after a time interval \f$ \Delta t \f$
according to the given discretization. This method can be
overridden in derived classes which want to hard-code a
particular discretization.
*/
virtual Disposable<Array> expectation(Time t0,
const Array& x0,
Time dt) const;
/*! returns the standard deviation
\f$ S(\mathrm{x}_{t_0 + \Delta t}
| \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
of the process after a time interval \f$ \Delta t \f$
according to the given discretization. This method can be
overridden in derived classes which want to hard-code a
particular discretization.
*/
virtual Disposable<Matrix> stdDeviation(Time t0,
const Array& x0,
Time dt) const;
/*! returns the covariance
\f$ V(\mathrm{x}_{t_0 + \Delta t}
| \mathrm{x}_{t_0} = \mathrm{x}_0) \f$
of the process after a time interval \f$ \Delta t \f$
according to the given discretization. This method can be
overridden in derived classes which want to hard-code a
particular discretization.
*/
virtual Disposable<Matrix> covariance(Time t0,
const Array& x0,
Time dt) const;
/*! returns the asset value after a time interval \f$ \Delta t
\f$ according to the given discretization. By default, it
returns
\f[
E(\mathrm{x}_0,t_0,\Delta t) +
S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w}
\f]
where \f$ E \f$ is the expectation and \f$ S \f$ the
standard deviation.
*/
virtual Disposable<Array> evolve(Time t0,
const Array& x0,
Time dt,
const Array& dw) const;
/*! applies a change to the asset value. By default, it
returns \f$ \mathrm{x} + \Delta \mathrm{x} \f$.
*/
virtual Disposable<Array> apply(const Array& x0,
const Array& dx) const;
//@}
//! \name utilities
//@{
/*! returns the time value corresponding to the given date
in the reference system of the stochastic process.
\note As a number of processes might not need this
functionality, a default implementation is given
which raises an exception.
*/
virtual Time time(const Date&) const;
//@}
//! \name Observer interface
//@{
void update();
//@}
protected:
StochasticProcess();
StochasticProcess(const boost::shared_ptr<discretization>&);
boost::shared_ptr<discretization> discretization_;
};
//! 1-dimensional stochastic process
/*! This class describes a stochastic process governed by
\f[
dx_t = \mu(t, x_t)dt + \sigma(t, x_t)dW_t.
\f]
*/
class StochasticProcess1D : public StochasticProcess {
public:
//! discretization of a 1-D stochastic process
class discretization {
public:
virtual ~discretization() {}
virtual Real drift(const StochasticProcess1D&,
Time t0, Real x0, Time dt) const = 0;
virtual Real diffusion(const StochasticProcess1D&,
Time t0, Real x0, Time dt) const = 0;
virtual Real variance(const StochasticProcess1D&,
Time t0, Real x0, Time dt) const = 0;
};
//! \name 1-D stochastic process interface
//@{
//! returns the initial value of the state variable
virtual Real x0() const = 0;
//! returns the drift part of the equation, i.e. \f$ \mu(t, x_t) \f$
virtual Real drift(Time t, Real x) const = 0;
/*! \brief returns the diffusion part of the equation, i.e.
\f$ \sigma(t, x_t) \f$
*/
virtual Real diffusion(Time t, Real x) const = 0;
/*! returns the expectation
\f$ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$
of the process after a time interval \f$ \Delta t \f$
according to the given discretization. This method can be
overridden in derived classes which want to hard-code a
particular discretization.
*/
virtual Real expectation(Time t0, Real x0, Time dt) const;
/*! returns the standard deviation
\f$ S(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$
of the process after a time interval \f$ \Delta t \f$
according to the given discretization. This method can be
overridden in derived classes which want to hard-code a
particular discretization.
*/
virtual Real stdDeviation(Time t0, Real x0, Time dt) const;
/*! returns the variance
\f$ V(x_{t_0 + \Delta t} | x_{t_0} = x_0) \f$
of the process after a time interval \f$ \Delta t \f$
according to the given discretization. This method can be
overridden in derived classes which want to hard-code a
particular discretization.
*/
virtual Real variance(Time t0, Real x0, Time dt) const;
/*! returns the asset value after a time interval \f$ \Delta t
\f$ according to the given discretization. By default, it
returns
\f[
E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w
\f]
where \f$ E \f$ is the expectation and \f$ S \f$ the
standard deviation.
*/
virtual Real evolve(Time t0, Real x0, Time dt, Real dw) const;
/*! applies a change to the asset value. By default, it
returns \f$ x + \Delta x \f$.
*/
virtual Real apply(Real x0, Real dx) const;
//@}
protected:
StochasticProcess1D();
StochasticProcess1D(const boost::shared_ptr<discretization>&);
boost::shared_ptr<discretization> discretization_;
private:
// StochasticProcess interface implementation
Size size() const;
Disposable<Array> initialValues() const;
Disposable<Array> drift(Time t, const Array& x) const;
Disposable<Matrix> diffusion(Time t, const Array& x) const;
Disposable<Array> expectation(Time t0, const Array& x0,
Time dt) const;
Disposable<Matrix> stdDeviation(Time t0, const Array& x0,
Time dt) const;
Disposable<Matrix> covariance(Time t0, const Array& x0,
Time dt) const;
Disposable<Array> evolve(Time t0, const Array& x0,
Time dt, const Array& dw) const;
Disposable<Array> apply(const Array& x0, const Array& dx) const;
};
// inline definitions
inline Size StochasticProcess1D::size() const {
return 1;
}
inline Disposable<Array> StochasticProcess1D::initialValues() const {
Array a(1, x0());
return a;
}
inline Disposable<Array> StochasticProcess1D::drift(
Time t, const Array& x) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(x.size() == 1, "1-D array required");
#endif
Array a(1, drift(t, x[0]));
return a;
}
inline Disposable<Matrix> StochasticProcess1D::diffusion(
Time t, const Array& x) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(x.size() == 1, "1-D array required");
#endif
Matrix m(1, 1, diffusion(t, x[0]));
return m;
}
inline Disposable<Array> StochasticProcess1D::expectation(
Time t0, const Array& x0, Time dt) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(x0.size() == 1, "1-D array required");
#endif
Array a(1, expectation(t0, x0[0], dt));
return a;
}
inline Disposable<Matrix> StochasticProcess1D::stdDeviation(
Time t0, const Array& x0, Time dt) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(x0.size() == 1, "1-D array required");
#endif
Matrix m(1, 1, stdDeviation(t0, x0[0], dt));
return m;
}
inline Disposable<Matrix> StochasticProcess1D::covariance(
Time t0, const Array& x0, Time dt) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(x0.size() == 1, "1-D array required");
#endif
Matrix m(1, 1, variance(t0, x0[0], dt));
return m;
}
inline Disposable<Array> StochasticProcess1D::evolve(
Time t0, const Array& x0,
Time dt, const Array& dw) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(x0.size() == 1, "1-D array required");
QL_REQUIRE(dw.size() == 1, "1-D array required");
#endif
Array a(1, evolve(t0,x0[0],dt,dw[0]));
return a;
}
inline Disposable<Array> StochasticProcess1D::apply(
const Array& x0,
const Array& dx) const {
#if defined(QL_EXTRA_SAFETY_CHECKS)
QL_REQUIRE(x0.size() == 1, "1-D array required");
QL_REQUIRE(dx.size() == 1, "1-D array required");
#endif
Array a(1, apply(x0[0],dx[0]));
return a;
}
}
#endif
|