GeneralizedBlackScholesProcess Class Reference

Generalized Black-Scholes stochastic process. More...

#include <ql/processes/blackscholesprocess.hpp>

Inheritance diagram for GeneralizedBlackScholesProcess:

Public Member Functions
	GeneralizedBlackScholesProcess (Handle< Quote > x0, Handle< YieldTermStructure > dividendTS, Handle< YieldTermStructure > riskFreeTS, Handle< BlackVolTermStructure > blackVolTS, const ext::shared_ptr< discretization > &d=ext::shared_ptr< discretization >(new EulerDiscretization), bool forceDiscretization=false)
	GeneralizedBlackScholesProcess (Handle< Quote > x0, Handle< YieldTermStructure > dividendTS, Handle< YieldTermStructure > riskFreeTS, Handle< BlackVolTermStructure > blackVolTS, Handle< LocalVolTermStructure > localVolTS)
StochasticProcess1D interface
Real	x0 () const override
	returns the initial value of the state variable
Real	drift (Time t, Real x) const override
Real	diffusion (Time t, Real x) const override
Real	apply (Real x0, Real dx) const override
Real	expectation (Time t0, Real x0, Time dt) const override
Real	stdDeviation (Time t0, Real x0, Time dt) const override
Real	variance (Time t0, Real x0, Time dt) const override
Real	evolve (Time t0, Real x0, Time dt, Real dw) const override
Time	time (const Date &) const override
Observer interface
void	update () override
Public Member Functions inherited from StochasticProcess
virtual Size	factors () const
	returns the number of independent factors of the process
void	update () override
Public Member Functions inherited from Observer
	Observer (const Observer &)
Observer &	operator= (const Observer &)
std::pair< iterator, bool >	registerWith (const ext::shared_ptr< Observable > &)
void	registerWithObservables (const ext::shared_ptr< Observer > &)
Size	unregisterWith (const ext::shared_ptr< Observable > &)
void	unregisterWithAll ()
virtual void	deepUpdate ()
Public Member Functions inherited from Observable
	Observable (const Observable &)
Observable &	operator= (const Observable &)
	Observable (Observable &&)=delete
Observable &	operator= (Observable &&)=delete
void	notifyObservers ()

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

Additional Inherited Members
Public Types inherited from Observer
typedef set_type::iterator	iterator
	StochasticProcess1D (ext::shared_ptr< discretization >)
	StochasticProcess (ext::shared_ptr< discretization >)
ext::shared_ptr< discretization >	discretization_
ext::shared_ptr< discretization >	discretization_

Detailed Description

Generalized Black-Scholes stochastic process.

This class describes the stochastic process \( S \) governed by

\[ d\ln S(t) = (r(t) - q(t) - \frac{\sigma(t, S)^2}{2}) dt + \sigma dW_t. \]

Warning

while the interface is expressed in terms of \( S \), the internal calculations work on \( ln S \).

Member Function Documentation

x0()

Real x0 ( ) const

overridevirtual

returns the initial value of the state variable

Implements StochasticProcess1D.

drift()

Real drift ( Time t, Real x ) const

overridevirtual

Implements StochasticProcess1D.

diffusion()

Real diffusion ( Time t, Real x ) const

overridevirtual

Implements StochasticProcess1D.

Reimplemented in VegaStressedBlackScholesProcess.

apply()

Real apply ( Real x0, Real dx ) const

overridevirtual

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

Reimplemented from StochasticProcess1D.

expectation()

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

overridevirtual

Warning

in general 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.

stdDeviation()

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

overridevirtual

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.

variance()

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

overridevirtual

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.

evolve()

Real evolve ( Time t0, Real x0, Time dt, Real dw ) const

overridevirtual

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 time ( const Date & ) const

overridevirtual

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.

update()

void update ( )

overridevirtual

This method must be implemented in derived classes. An instance of Observer does not call this method directly: instead, it will be called by the observables the instance registered with when they need to notify any changes.

Implements Observer.