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Public Member Functions | List of all members
OrnsteinUhlenbeckProcess Class Reference

Ornstein-Uhlenbeck process class. More...

#include <ornsteinuhlenbeckprocess.hpp>

+ Inheritance diagram for OrnsteinUhlenbeckProcess:
+ Collaboration diagram for OrnsteinUhlenbeckProcess:

Public Member Functions

 OrnsteinUhlenbeckProcess (Real speed, Volatility 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 &)
 
Observeroperator= (const Observer &)
 
virtual ~Observer ()
 
std::pair< iterator, boolregisterWith (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 &)
 
Observableoperator= (const Observable &)
 
 Observable (Observable &&)=delete
 
Observableoperator= (Observable &&)=delete
 
virtual ~Observable ()=default
 
void notifyObservers ()
 

StochasticProcess interface

Real x0_
 
Real speed_
 
Real level_
 
Volatility volatility_
 
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 x0 () const override
 returns the initial value of the state variable More...
 
Real speed () const
 
Real volatility () const
 
Real level () const
 
Real variance (Time t0, Real x0, Time dt) const override
 

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< discretizationdiscretization_
 
- Protected Attributes inherited from StochasticProcess
ext::shared_ptr< discretizationdiscretization_
 

Detailed Description

Ornstein-Uhlenbeck process class.

This class describes the Ornstein-Uhlenbeck process governed by

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

Definition at line 41 of file ornsteinuhlenbeckprocess.hpp.

Constructor & Destructor Documentation

◆ OrnsteinUhlenbeckProcess()

OrnsteinUhlenbeckProcess ( Real  speed,
Volatility  vol,
Real  x0 = 0.0,
Real  level = 0.0 
)

Definition at line 26 of file ornsteinuhlenbeckprocess.cpp.

Member Function Documentation

◆ 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 83 of file ornsteinuhlenbeckprocess.hpp.

◆ 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 87 of file ornsteinuhlenbeckprocess.hpp.

◆ 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 91 of file ornsteinuhlenbeckprocess.hpp.

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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 96 of file ornsteinuhlenbeckprocess.hpp.

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◆ x0()

Real x0 ( ) const
overridevirtual

returns the initial value of the state variable

Implements StochasticProcess1D.

Definition at line 67 of file ornsteinuhlenbeckprocess.hpp.

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◆ speed()

Real speed ( ) const

Definition at line 71 of file ornsteinuhlenbeckprocess.hpp.

◆ volatility()

Real volatility ( ) const

Definition at line 75 of file ornsteinuhlenbeckprocess.hpp.

◆ level()

Real level ( ) const

Definition at line 79 of file ornsteinuhlenbeckprocess.hpp.

◆ 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 34 of file ornsteinuhlenbeckprocess.cpp.

Member Data Documentation

◆ x0_

Real x0_
private

Definition at line 61 of file ornsteinuhlenbeckprocess.hpp.

◆ speed_

Real speed_
private

Definition at line 61 of file ornsteinuhlenbeckprocess.hpp.

◆ level_

Real level_
private

Definition at line 61 of file ornsteinuhlenbeckprocess.hpp.

◆ volatility_

Volatility volatility_
private

Definition at line 62 of file ornsteinuhlenbeckprocess.hpp.