StochasticProcess Class Reference

multi-dimensional stochastic process class. More...

#include <ql/stochasticprocess.hpp>

Inheritance diagram for StochasticProcess:

Classes
class	discretization
	discretization of a stochastic process over a given time interval More...

Public Member Functions
Stochastic process interface
virtual Size	size () const =0
	returns the number of dimensions of the stochastic process
virtual Size	factors () const
	returns the number of independent factors of the process
virtual Disposable< Array >	initialValues () const =0
	returns the initial values of the state variables
virtual Disposable< Array >	drift (Time t, const Array &x) const =0
	returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
virtual Disposable< Matrix >	diffusion (Time t, const Array &x) const =0
	returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)
virtual Disposable< Array >	expectation (Time t0, const Array &x0, Time dt) const
virtual Disposable< Matrix >	stdDeviation (Time t0, const Array &x0, Time dt) const
virtual Disposable< Matrix >	covariance (Time t0, const Array &x0, Time dt) const
virtual Disposable< Array >	evolve (Time t0, const Array &x0, Time dt, const Array &dw) const
virtual Disposable< Array >	apply (const Array &x0, const Array &dx) const
utilities
virtual Time	time (const Date &) const
Observer interface
void	update ()
Public Member Functions inherited from Observer
	Observer (const Observer &)
Observer &	operator= (const Observer &)
std::pair< iterator, bool >	registerWith (const boost::shared_ptr< Observable > &)
void	registerWithObservables (const boost::shared_ptr< Observer > &)
Size	unregisterWith (const boost::shared_ptr< Observable > &)
void	unregisterWithAll ()
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
void	notifyObservers ()

Protected Member Functions
	StochasticProcess (const boost::shared_ptr< discretization > &)

Protected Attributes
boost::shared_ptr< discretization >	discretization_

Additional Inherited Members
Public Types inherited from Observer
typedef std::set< boost::shared_ptr< Observable > >	set_type
typedef set_type::iterator	iterator

Detailed Description

multi-dimensional stochastic process class.

This class describes a stochastic process governed by

\[ d\mathrm{x}_t = \mu(t, x_t)\mathrm{d}t + \sigma(t, \mathrm{x}_t) \cdot d\mathrm{W}_t. \]

Member Function Documentation

virtual Disposable<Array> expectation ( Time  t0, const Array &  x0, Time  dt  ) const

virtual

returns the expectation \( E(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

Reimplemented in G2ForwardProcess, StochasticProcessArray, and G2Process.

virtual Disposable<Matrix> stdDeviation ( Time  t0, const Array &  x0, Time  dt  ) const

virtual

returns the standard deviation \( S(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

Reimplemented in G2ForwardProcess, StochasticProcessArray, and G2Process.

virtual Disposable<Matrix> covariance ( Time  t0, const Array &  x0, Time  dt  ) const

virtual

returns the covariance \( V(\mathrm{x}_{t_0 + \Delta t} | \mathrm{x}_{t_0} = \mathrm{x}_0) \) of the process after a time interval \( \Delta t \) according to the given discretization. This method can be overridden in derived classes which want to hard-code a particular discretization.

Reimplemented in G2ForwardProcess, LiborForwardModelProcess, StochasticProcessArray, and G2Process.

virtual Disposable<Array> evolve ( Time  t0, const Array &  x0, Time  dt, const Array &  dw  ) const

virtual

returns the asset value after a time interval \( \Delta t \) according to the given discretization. By default, it returns

\[ E(\mathrm{x}_0,t_0,\Delta t) + S(\mathrm{x}_0,t_0,\Delta t) \cdot \Delta \mathrm{w} \]

where \( E \) is the expectation and \( S \) the standard deviation.

Reimplemented in GJRGARCHProcess, HestonProcess, ExtOUWithJumpsProcess, LiborForwardModelProcess, KlugeExtOUProcess, BatesProcess, HybridHestonHullWhiteProcess, and StochasticProcessArray.

virtual Disposable<Array> apply ( const Array &  x0, const Array &  dx  ) const

virtual

applies a change to the asset value. By default, it returns \( \mathrm{x} + \Delta \mathrm{x} \).

Reimplemented in GJRGARCHProcess, HestonProcess, LiborForwardModelProcess, HybridHestonHullWhiteProcess, and StochasticProcessArray.

virtual Time time ( const Date &  ) const

virtual

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.

Reimplemented in GJRGARCHProcess, HestonProcess, GeneralizedBlackScholesProcess, HybridHestonHullWhiteProcess, Merton76Process, StochasticProcessArray, and GsrProcess.

void update ( )

virtual

This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.

Implements Observer.