QuantLib::OrnsteinUhlenbeckProcess

OrnsteinUhlenbeckProcess Class Reference

#include <ql/Processes/ornsteinuhlenbeckprocess.hpp>

Inheritance diagram for OrnsteinUhlenbeckProcess:

[legend]List of all members.

Detailed Description

Ornstein-Uhlenbeck process class.

This class describes the Ornstein-Uhlenbeck process governed by

$dx = -a x_t dt + \sigma dW_t.$

Public Member Functions

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

StochasticProcess interface

Real x0 () const

returns the initial value of the state variable

Real drift (Time t, Real x) const

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

Real diffusion (Time t, Real x) const

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

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

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

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

Member Function Documentation

Real expectation ( Time t0,

Real x0,

Time dt

) const [virtual]

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.

Real stdDeviation ( Time t0,

Real x0,

Time dt

) const [virtual]

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.

Real variance ( Time t0,

Real x0,

Time dt

) const [virtual]

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.

QuantLib 0.3.12

Getting started

Reference manual

OrnsteinUhlenbeckProcess Class Reference

Detailed Description

Public Member Functions

Member Function Documentation


Public Member Functions
	OrnsteinUhlenbeckProcess (Real speed, Volatility vol, Real x0=0.0)
StochasticProcess interface
Real	x0 () const
	returns the initial value of the state variable
Real	drift (Time t, Real x) const
	returns the drift part of the equation, i.e. $\mu(t, x_t)$
Real	diffusion (Time t, Real x) const
	returns the diffusion part of the equation, i.e. $\sigma(t, x_t)$
Real	expectation (Time t0, Real x0, Time dt) const
Real	stdDeviation (Time t0, Real x0, Time dt) const
Real	variance (Time t0, Real x0, Time dt) const