OrnsteinUhlenbeckProcess Class Reference

#include <diffusionprocess.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 (double speed, double vol, double x0=0.0)
double drift (Time t, double x) const
 returns the drift part of the equation, i.e. $ \mu(t, x_t) $

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

double expectation (Time t0, double x0, Time dt) const
 returns the expectation of the process after a time interval

double variance (Time t0, double x0, Time dt) const
 returns the variance of the process after a time interval


Member Function Documentation

double expectation Time  t0,
double  x0,
Time  dt
const [virtual]
 

returns the expectation of the process after a time interval

returns $ E(x_{t_0 + \Delta t} | x_{t_0} = x_0) $. By default, it returns the Euler approximation defined by $ x_0 + \mu(t_0, x_0) \Delta t $.

Reimplemented from DiffusionProcess.

double variance Time  t0,
double  x0,
Time  dt
const [virtual]
 

returns the variance of the process after a time interval

returns $ Var(x_{t_0 + \Delta t} | x_{t_0} = x_0) $. By default, it returns the Euler approximation defined by $ \sigma(t_0, x_0)^2 \Delta t $.

Reimplemented from DiffusionProcess.


The documentation for this class was generated from the following file:

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