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

Observer interface
ext::shared_ptr< discretization >	discretization_
void	update () override
	StochasticProcess (ext::shared_ptr< discretization >)

Additional Inherited Members
Public Types inherited from Observer
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

size()

virtual Size size ( ) const

pure virtual

returns the number of dimensions of the stochastic process

Implemented in ExtOUWithJumpsProcess, G2ForwardProcess, G2Process, GJRGARCHProcess, HestonProcess, HybridHestonHullWhiteProcess, KlugeExtOUProcess, LiborForwardModelProcess, and StochasticProcessArray.

factors()

virtual Size factors ( ) const

virtual

returns the number of independent factors of the process

Reimplemented in BatesProcess, ExtOUWithJumpsProcess, HestonProcess, KlugeExtOUProcess, and LiborForwardModelProcess.

initialValues()

virtual Array initialValues ( ) const

pure virtual

returns the initial values of the state variables

Implemented in ExtOUWithJumpsProcess, G2ForwardProcess, G2Process, GJRGARCHProcess, HestonProcess, HybridHestonHullWhiteProcess, KlugeExtOUProcess, LiborForwardModelProcess, and StochasticProcessArray.

drift()

virtual Array drift ( Time t, const Array & x ) const

pure virtual

returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)

Implemented in BatesProcess, ExtOUWithJumpsProcess, G2ForwardProcess, G2Process, GJRGARCHProcess, HestonProcess, HybridHestonHullWhiteProcess, KlugeExtOUProcess, LiborForwardModelProcess, and StochasticProcessArray.

diffusion()

virtual Matrix diffusion ( Time t, const Array & x ) const

pure virtual

returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)

Implemented in ExtOUWithJumpsProcess, G2ForwardProcess, G2Process, GJRGARCHProcess, HestonProcess, HybridHestonHullWhiteProcess, KlugeExtOUProcess, LiborForwardModelProcess, and StochasticProcessArray.

expectation()

virtual 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, G2Process, and StochasticProcessArray.

stdDeviation()

virtual 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, G2Process, and StochasticProcessArray.

covariance()

virtual 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, G2Process, LiborForwardModelProcess, and StochasticProcessArray.

evolve()

virtual 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 BatesProcess, ExtOUWithJumpsProcess, GJRGARCHProcess, HestonProcess, HybridHestonHullWhiteProcess, KlugeExtOUProcess, LiborForwardModelProcess, and StochasticProcessArray.

apply()

virtual 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, HybridHestonHullWhiteProcess, LiborForwardModelProcess, and StochasticProcessArray.

time()

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

update()

void update ( )

overridevirtual

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.