Extended Ornstein-Uhlenbeck process class. More...

#include <extendedornsteinuhlenbeckprocess.hpp>

Inheritance diagram for ExtendedOrnsteinUhlenbeckProcess:

Collaboration diagram for ExtendedOrnsteinUhlenbeckProcess:

Public Types
enum	Discretization { MidPoint , Trapezodial , GaussLobatto }

Public Types inherited from Observer
typedef set_type::iterator	iterator

Public Member Functions
	ExtendedOrnsteinUhlenbeckProcess (Real speed, Volatility sigma, Real x0, ext::function< Real(Real)> b, Discretization discretization=MidPoint, Real intEps=1e-4)

Public Member Functions inherited from StochasticProcess1D
virtual Real	evolve (Time t0, Real x0, Time dt, Real dw) const

virtual Real	apply (Real x0, Real dx) const

Public Member Functions inherited from StochasticProcess
	~StochasticProcess () override=default

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

virtual Time	time (const Date &) const

void	update () override

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 ()

StochasticProcess interface
const Real	speed_

const Volatility	vol_

const ext::function< Real(Real)>	b_

const Real	intEps_

const ext::shared_ptr< OrnsteinUhlenbeckProcess >	ouProcess_

const Discretization	discretization_

Real	x0 () const override
	returns the initial value of the state variable More...

Real	speed () const

Real	volatility () const

Real	drift (Time t, Real x) const override
	returns the drift part of the equation, i.e. \( \mu(t, x_t) \) More...

Real	diffusion (Time t, Real x) const override
	returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \) More...

Real	expectation (Time t0, Real x0, Time dt) const override

Real	stdDeviation (Time t0, Real x0, Time dt) const override

Real	variance (Time t0, Real x0, Time dt) const override

Additional Inherited Members
Protected Member Functions inherited from StochasticProcess1D
	StochasticProcess1D ()=default

	StochasticProcess1D (ext::shared_ptr< discretization >)

Protected Member Functions inherited from StochasticProcess
	StochasticProcess ()=default

	StochasticProcess (ext::shared_ptr< discretization >)

Protected Attributes inherited from StochasticProcess1D
ext::shared_ptr< discretization >	discretization_

Protected Attributes inherited from StochasticProcess
ext::shared_ptr< discretization >	discretization_

Detailed Description

Extended Ornstein-Uhlenbeck process class.

This class describes the Ornstein-Uhlenbeck process governed by

\[ dx = a (b(t) - x_t) dt + \sigma dW_t. \]

Definition at line 42 of file extendedornsteinuhlenbeckprocess.hpp.

Member Enumeration Documentation

◆ Discretization

enum Discretization

Enumerator
MidPoint
Trapezodial
GaussLobatto

Definition at line 44 of file extendedornsteinuhlenbeckprocess.hpp.

Constructor & Destructor Documentation

◆ ExtendedOrnsteinUhlenbeckProcess()

ExtendedOrnsteinUhlenbeckProcess	(	Real	speed,
		Volatility	sigma,
		Real	x0,
		ext::function< Real(Real)>	b,
		Discretization	discretization = `MidPoint`,
		Real	intEps = `1e-4`
	)

Definition at line 41 of file extendedornsteinuhlenbeckprocess.cpp.

Member Function Documentation

◆ x0()

Real x0 ( ) const

overridevirtual

returns the initial value of the state variable

Implements StochasticProcess1D.

Definition at line 54 of file extendedornsteinuhlenbeckprocess.cpp.

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◆ speed()

Real speed ( ) const

Definition at line 76 of file extendedornsteinuhlenbeckprocess.cpp.

◆ volatility()

Real volatility ( ) const

Definition at line 80 of file extendedornsteinuhlenbeckprocess.cpp.

◆ drift()

Real drift	(	Time	t,
		Real	x
	)		const

overridevirtual

returns the drift part of the equation, i.e. \( \mu(t, x_t) \)

Implements StochasticProcess1D.

Definition at line 58 of file extendedornsteinuhlenbeckprocess.cpp.

◆ diffusion()

Real diffusion	(	Time	t,
		Real	x
	)		const

overridevirtual

returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \)

Implements StochasticProcess1D.

Definition at line 62 of file extendedornsteinuhlenbeckprocess.cpp.

◆ expectation()

Real expectation	(	Time	t0,
		Real	x0,
		Time	dt
	)		const

overridevirtual

returns the expectation \( E(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) 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 from StochasticProcess1D.

Definition at line 84 of file extendedornsteinuhlenbeckprocess.cpp.

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◆ stdDeviation()

Real stdDeviation	(	Time	t0,
		Real	x0,
		Time	dt
	)		const

overridevirtual

returns the standard deviation \( S(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) 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 from StochasticProcess1D.

Definition at line 66 of file extendedornsteinuhlenbeckprocess.cpp.

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◆ variance()

Real variance	(	Time	t0,
		Real	x0,
		Time	dt
	)		const

overridevirtual

returns the variance \( V(x_{t_0 + \Delta t} | x_{t_0} = x_0) \) 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 from StochasticProcess1D.

Definition at line 71 of file extendedornsteinuhlenbeckprocess.cpp.

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