QuantLib_ExtendedOrnsteinUhlenbeckProcess man page

ExtendedOrnsteinUhlenbeckProcess — Extended Ornstein-Uhlenbeck process class.

Synopsis

`#include <ql/experimental/processes/extendedornsteinuhlenbeckprocess.hpp>`

Inherits StochasticProcess1D.

Public Types

enum Discretization { MidPoint, Trapezodial, GaussLobatto }

Public Member Functions

ExtendedOrnsteinUhlenbeckProcess (Real speed, Volatility sigma, Real x0, const boost::function< Real(Real)> &b, Discretization discretization=MidPoint, Real intEps=1e-4)

StochasticProcess interface

Real x0 () const
returns the initial value of the state variable
Real speed () const
Real volatility () 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. \$ 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

Detailed Description

Extended Ornstein-Uhlenbeck process class.

This class describes the Ornstein-Uhlenbeck process governed by [ dx = a (b(t) - x_t) dt + sigma 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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Referenced By

The man pages expectation(3), ExtendedOrnsteinUhlenbeckProcess(3) and speed(3) are aliases of QuantLib_ExtendedOrnsteinUhlenbeckProcess(3).

Mon Apr 30 2018 Version 1.12.1 QuantLib