QuantLib
A free/open-source library for quantitative finance
Reference manual - version 1.20
Classes | List of all members
StochasticProcess Class Referenceabstract

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< ArrayinitialValues () const =0
 returns the initial values of the state variables
 
virtual Disposable< Arraydrift (Time t, const Array &x) const =0
 returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \)
 
virtual Disposable< Matrixdiffusion (Time t, const Array &x) const =0
 returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \)
 
virtual Disposable< Arrayexpectation (Time t0, const Array &x0, Time dt) const
 
virtual Disposable< MatrixstdDeviation (Time t0, const Array &x0, Time dt) const
 
virtual Disposable< Matrixcovariance (Time t0, const Array &x0, Time dt) const
 
virtual Disposable< Arrayevolve (Time t0, const Array &x0, Time dt, const Array &dw) const
 
virtual Disposable< Arrayapply (const Array &x0, const Array &dx) const
 
utilities
virtual Time time (const Date &) const
 
- Public Member Functions inherited from Observer
 Observer (const Observer &)
 
Observeroperator= (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 &)
 
Observableoperator= (const Observable &)
 
void notifyObservers ()
 

Observer interface

ext::shared_ptr< discretizationdiscretization_
 
void update ()
 
 StochasticProcess ()
 
 StochasticProcess (const ext::shared_ptr< discretization > &)
 

Additional Inherited Members

- Public Types inherited from Observer
typedef boost::unordered_set< ext::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

◆ expectation()

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 StochasticProcessArray, G2ForwardProcess, and G2Process.

◆ stdDeviation()

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 StochasticProcessArray, G2ForwardProcess, and G2Process.

◆ covariance()

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 StochasticProcessArray, G2ForwardProcess, G2Process, and LiborForwardModelProcess.

◆ evolve()

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

◆ apply()

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 StochasticProcessArray, HybridHestonHullWhiteProcess, HestonProcess, GJRGARCHProcess, and LiborForwardModelProcess.

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

◆ update()

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.