/usr/include/ql/stochasticprocess.hpp is in libquantlib0-dev 1.4-2+b1.
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/*
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
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