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level: Ornstein-Uhlenbeck process class.

NAME

QuantLib::OrnsteinUhlenbeckProcess - Ornstein-Uhlenbeck process class.

SYNOPSIS

#include <ql/processes/ornsteinuhlenbeckprocess.hpp>

Inherits QuantLib::StochasticProcess1D.

Public Member Functions

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

StochasticProcess interface

Real x0 () const
returns the initial value of the state variable
Real speed () const

Real volatility () const

Real level () const

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. $ igma(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

Detailed Description

Ornstein-Uhlenbeck process class.

This class describes the Ornstein-Uhlenbeck process governed by [ dx = a (r - x_t) dt + igma dW_t. ]

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.

Author

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