ExtendedBlackScholesMertonProcess Class Reference

experimental Black-Scholes-Merton stochastic process More...

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

Inheritance diagram for ExtendedBlackScholesMertonProcess:

Public Types

enum  Discretization { Euler, Milstein, PredictorCorrector }
 

Public Member Functions

 ExtendedBlackScholesMertonProcess (const Handle< Quote > &x0, const Handle< YieldTermStructure > &dividendTS, const Handle< YieldTermStructure > &riskFreeTS, const Handle< BlackVolTermStructure > &blackVolTS, const boost::shared_ptr< discretization > &d=boost::shared_ptr< discretization >(new EulerDiscretization), Discretization evolDisc=Milstein)
 
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 evolve (Time t0, Real x0, Time dt, Real dw) const
 
- Public Member Functions inherited from GeneralizedBlackScholesProcess
 GeneralizedBlackScholesProcess (const Handle< Quote > &x0, const Handle< YieldTermStructure > &dividendTS, const Handle< YieldTermStructure > &riskFreeTS, const Handle< BlackVolTermStructure > &blackVolTS, const boost::shared_ptr< discretization > &d=boost::shared_ptr< discretization >(new EulerDiscretization))
 
Time time (const Date &) const
 
Real x0 () const
 returns the initial value of the state variable
 
Real drift (Time t, Real x) const
 
Real diffusion (Time t, Real x) const
 
Real apply (Real x0, Real dx) const
 
Real expectation (Time t0, Real x0, Time dt) const
 
Real evolve (Time t0, Real x0, Time dt, Real dw) const
 
void update ()
 
const Handle< Quote > & stateVariable () const
 
const Handle
< YieldTermStructure > & 
dividendYield () const
 
const Handle
< YieldTermStructure > & 
riskFreeRate () const
 
const Handle
< BlackVolTermStructure > & 
blackVolatility () const
 
const Handle
< LocalVolTermStructure > & 
localVolatility () const
 
- Public Member Functions inherited from StochasticProcess1D
virtual Real stdDeviation (Time t0, Real x0, Time dt) const
 
virtual Real variance (Time t0, Real x0, Time dt) const
 
- Public Member Functions inherited from StochasticProcess
virtual Size factors () const
 returns the number of independent factors of the process
 
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 Attributes inherited from StochasticProcess1D
boost::shared_ptr< discretizationdiscretization_
 

Detailed Description

experimental Black-Scholes-Merton stochastic process

This class allows to choose a built-in discretization scheme

Member Function Documentation

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.