GemanRoncoroniProcess Class Reference

Geman-Roncoroni process class. More...

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

Inheritance diagram for GemanRoncoroniProcess:

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
 
- Public Member Functions inherited from StochasticProcess1D
virtual Real expectation (Time t0, Real x0, Time dt) const
 
virtual Real variance (Time t0, Real x0, Time dt) const
 
virtual Real apply (Real x0, Real dx) const
 
- Public Member Functions inherited from StochasticProcess
virtual Size factors () const
 returns the number of independent factors of the process
 
virtual Time time (const Date &) const
 
void update ()
 
- Public Member Functions inherited from Observer
 Observer (const Observer &)
 
Observeroperator= (const Observer &)
 
std::pair< std::set
< boost::shared_ptr
< Observable > >::iterator,
bool > 
registerWith (const boost::shared_ptr< Observable > &)
 
Size unregisterWith (const boost::shared_ptr< Observable > &)
 
void unregisterWithAll ()
 
- Public Member Functions inherited from Observable
 Observable (const Observable &)
 
Observableoperator= (const Observable &)
 
void notifyObservers ()
 

Additional Inherited Members

- Protected Member Functions inherited from StochasticProcess1D
 StochasticProcess1D (const boost::shared_ptr< discretization > &)
 
- Protected Member Functions inherited from StochasticProcess
 StochasticProcess (const boost::shared_ptr< discretization > &)
 
- Protected Attributes inherited from StochasticProcess1D
boost::shared_ptr< discretizationdiscretization_
 
- Protected Attributes inherited from StochasticProcess
boost::shared_ptr< discretizationdiscretization_
 

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.