GemanRoncoroniProcess Class Reference

Geman-Roncoroni process class. More...

#include <ql/experimental/processes/gemanroncoroniprocess.hpp>

Inheritance diagram for GemanRoncoroniProcess:

List of all members.

Public Member Functions

 GemanRoncoroniProcess (Real x0, Real alpha, Real beta, Real gamma, Real delta, Real eps, Real zeta, Real d, Real k, Real tau, Real sig2, Real a, Real b, Real theta1, Real theta2, Real theta3, Real psi)
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 stdDeviation (Time t0, Real x0, Time dt) const
Real evolve (Time t0, Real x0, Time dt, Real dw) const
Real evolve (Time t0, Real x0, Time dt, Real dw, const Array &du) const

Detailed Description

Geman-Roncoroni process class.

This class describes the Geman-Roncoroni process governed by

\[ \begin{array}{rcl} dE(t) &=& \left[ \frac{\partial}{\partial t} \mu(t) +\theta_1 \left(\mu(t)-E(t^-)\right)\right]dt +\sigma dW(t) + h(E(t^-))dJ(t) \\ \mu(t)&=& \alpha + \beta t +\gamma \cos(\epsilon+2\pi t) +\delta \cos(\zeta + 4\pi t) \end{array} \]


Member Function Documentation

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 evolve ( Time  t0,
Real  x0,
Time  dt,
Real  dw 
) const [virtual]

returns the asset value after a time interval $ \Delta t $ according to the given discretization. By default, it returns

\[ E(x_0,t_0,\Delta t) + S(x_0,t_0,\Delta t) \cdot \Delta w \]

where $ E $ is the expectation and $ S $ the standard deviation.

Reimplemented from StochasticProcess1D.