Generalized Black-Scholes stochastic process. More...

#include <ql/processes/blackscholesprocess.hpp>

Inheritance diagram for GeneralizedBlackScholesProcess:

Public Member Functions
	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

StochasticProcess1D interface
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

Observer interface
void	update ()

Inspectors
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 &)

Observer &	operator= (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 &)

Observable &	operator= (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< discretization >	discretization_

Detailed Description

Generalized Black-Scholes stochastic process.

This class describes the stochastic process governed by

$dS(t, S) = (r(t) - q(t) - \frac{\sigma(t, S)^2}{2}) dt + \sigma dW_t.$

Member Function Documentation

Real drift	(	Time	t,
		Real	x
	)		const

virtual

Possible enhancements:: revise extrapolation

Implements StochasticProcess1D.

Real diffusion	(	Time	t,
		Real	x
	)		const

virtual

Possible enhancements:: revise extrapolation

Implements StochasticProcess1D.

Real apply	(	Real	x0,
		Real	dx
	)		const

virtual

applies a change to the asset value. By default, it returns $x + \Delta x$ .

Reimplemented from StochasticProcess1D.

Real expectation	(	Time	t0,
		Real	x0,
		Time	dt
	)		const

virtual

Warning:: raises a "not implemented" exception. It should be rewritten to return the expectation E(S) of the process, not exp(E(log S)).

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.

Time time ( const Date & ) const

virtual

returns the time value corresponding to the given date in the reference system of the stochastic process.

Note: As a number of processes might not need this functionality, a default implementation is given which raises an exception.

Reimplemented from StochasticProcess.

A free/open-source library for quantitative finance

Version 1.2.1

Getting started

Reference manual

Public Member Functions

Additional Inherited Members

Detailed Description

Member Function Documentation