OrnsteinUhlenbeckProcess Class Reference

#include <ql/stochasticprocess.hpp>

Inheritance diagram for OrnsteinUhlenbeckProcess:

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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 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 StochasticProcess.

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 StochasticProcess.


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