Piecewise linear Ornstein-Uhlenbeck process class. More...

#include <generalizedornsteinuhlenbeckprocess.hpp>

Inheritance diagram for GeneralizedOrnsteinUhlenbeckProcess:

Collaboration diagram for GeneralizedOrnsteinUhlenbeckProcess:

Public Member Functions
	GeneralizedOrnsteinUhlenbeckProcess (ext::function< Real(Time)> speed, ext::function< Real(Time)> vol, Real x0=0.0, Real level=0.0)

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 ()

StochasticProcess1D interface
Real	x0_

Real	level_

ext::function< Real(Time)>	speed_

ext::function< Real(Time)>	volatility_

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

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

Real	speed (Time t) const

Real	volatility (Time t) const

Real	level () const

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator

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

Piecewise linear Ornstein-Uhlenbeck process class.

This class describes the Ornstein-Uhlenbeck process governed by

\[ dx = a (level - x_t) dt + \sigma dW_t \]

where the coefficients a and sigma are piecewise linear.

Definition at line 43 of file generalizedornsteinuhlenbeckprocess.hpp.

Constructor & Destructor Documentation

◆ GeneralizedOrnsteinUhlenbeckProcess()

GeneralizedOrnsteinUhlenbeckProcess	(	ext::function< Real(Time)>	speed,
		ext::function< Real(Time)>	vol,
		Real	x0 = `0.0`,
		Real	level = `0.0`
	)

Definition at line 26 of file generalizedornsteinuhlenbeckprocess.cpp.

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Member Function Documentation

◆ x0()

Real x0 ( ) const

overridevirtual

returns the initial value of the state variable

Implements StochasticProcess1D.

Definition at line 34 of file generalizedornsteinuhlenbeckprocess.cpp.

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◆ 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 38 of file generalizedornsteinuhlenbeckprocess.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 42 of file generalizedornsteinuhlenbeckprocess.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 46 of file generalizedornsteinuhlenbeckprocess.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 51 of file generalizedornsteinuhlenbeckprocess.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 56 of file generalizedornsteinuhlenbeckprocess.cpp.