multi-dimensional stochastic process class. More...

#include <stochasticprocess.hpp>

Inheritance diagram for StochasticProcess:

Collaboration diagram for StochasticProcess:

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

Public Member Functions
	~StochasticProcess () override=default

Stochastic process interface
virtual Size	size () const =0
	returns the number of dimensions of the stochastic process More...

virtual Size	factors () const
	returns the number of independent factors of the process More...

virtual Array	initialValues () const =0
	returns the initial values of the state variables More...

virtual Array	drift (Time t, const Array &x) const =0
	returns the drift part of the equation, i.e., \( \mu(t, \mathrm{x}_t) \) More...

virtual Matrix	diffusion (Time t, const Array &x) const =0
	returns the diffusion part of the equation, i.e. \( \sigma(t, \mathrm{x}_t) \) More...

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 ()=default

	Observer (const Observer &)

Observer &	operator= (const Observer &)

virtual	~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	update ()=0

virtual void	deepUpdate ()

Public Member Functions inherited from Observable
	Observable ()

	Observable (const Observable &)

Observable &	operator= (const Observable &)

	Observable (Observable &&)=delete

Observable &	operator= (Observable &&)=delete

virtual	~Observable ()=default

void	notifyObservers ()

Observer interface
ext::shared_ptr< discretization >	discretization_

void	update () override

	StochasticProcess ()=default

	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

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

Definition at line 42 of file stochasticprocess.hpp.

Constructor & Destructor Documentation

◆ ~StochasticProcess()

~StochasticProcess ( )

overridedefault

◆ StochasticProcess() [1/2]

StochasticProcess ( )

protecteddefault

◆ StochasticProcess() [2/2]

StochasticProcess ( ext::shared_ptr< discretization > disc )

explicitprotected

Definition at line 29 of file stochasticprocess.cpp.

Member Function Documentation

◆ size()

virtual Size size ( ) const

pure virtual

returns the number of dimensions of the stochastic process

Implemented in ExtOUWithJumpsProcess, KlugeExtOUProcess, LiborForwardModelProcess, G2Process, G2ForwardProcess, GJRGARCHProcess, HestonProcess, HestonSLVProcess, HybridHestonHullWhiteProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

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◆ factors()

Size factors ( ) const

virtual

returns the number of independent factors of the process

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

Definition at line 32 of file stochasticprocess.cpp.

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◆ initialValues()

virtual Array initialValues ( ) const

pure virtual

returns the initial values of the state variables

Implemented in ExtOUWithJumpsProcess, KlugeExtOUProcess, LiborForwardModelProcess, G2Process, G2ForwardProcess, GJRGARCHProcess, HestonProcess, HestonSLVProcess, HybridHestonHullWhiteProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

◆ 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 ExtOUWithJumpsProcess, KlugeExtOUProcess, LiborForwardModelProcess, BatesProcess, G2Process, G2ForwardProcess, GJRGARCHProcess, HestonProcess, HestonSLVProcess, HybridHestonHullWhiteProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

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◆ 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, KlugeExtOUProcess, LiborForwardModelProcess, G2Process, G2ForwardProcess, GJRGARCHProcess, HestonProcess, HestonSLVProcess, HybridHestonHullWhiteProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

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◆ expectation()

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 G2Process, G2ForwardProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

Definition at line 36 of file stochasticprocess.cpp.

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◆ stdDeviation()

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 G2Process, G2ForwardProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

Definition at line 42 of file stochasticprocess.cpp.

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◆ covariance()

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 LiborForwardModelProcess, G2Process, G2ForwardProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

Definition at line 48 of file stochasticprocess.cpp.

◆ evolve()

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 GemanRoncoroniProcess, ExtOUWithJumpsProcess, KlugeExtOUProcess, LiborForwardModelProcess, BatesProcess, GJRGARCHProcess, HestonProcess, HestonSLVProcess, HybridHestonHullWhiteProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

Definition at line 54 of file stochasticprocess.cpp.

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◆ apply()

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 LiborForwardModelProcess, GJRGARCHProcess, HestonProcess, HestonSLVProcess, HybridHestonHullWhiteProcess, JointStochasticProcess, StochasticProcessArray, and StochasticProcess1D.

Definition at line 59 of file stochasticprocess.cpp.

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◆ time()

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, HestonProcess, Merton76Process, StochasticProcessArray, GsrProcess, HestonSLVProcess, HybridHestonHullWhiteProcess, and JointStochasticProcess.

Definition at line 64 of file stochasticprocess.cpp.

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◆ 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.

Definition at line 68 of file stochasticprocess.cpp.

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Member Data Documentation

◆ discretization_

ext::shared_ptr<discretization> discretization_

protected

Definition at line 153 of file stochasticprocess.hpp.

Classes

Public Member Functions

Observer interface

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ ~StochasticProcess()

◆ StochasticProcess() [1/2]

◆ StochasticProcess() [2/2]

Member Function Documentation

◆ size()

◆ factors()

◆ initialValues()

◆ drift()

◆ diffusion()

◆ expectation()

◆ stdDeviation()

◆ covariance()

◆ evolve()

◆ apply()

◆ time()

◆ update()

Member Data Documentation

◆ discretization_