BlackScholesProcess Class Reference

Black-Scholes (1973) stochastic process. More...

#include <ql/processes/blackscholesprocess.hpp>

Inheritance diagram for BlackScholesProcess:

Public Member Functions
	BlackScholesProcess (const Handle< Quote > &x0, const Handle< YieldTermStructure > &riskFreeTS, const Handle< BlackVolTermStructure > &blackVolTS, const ext::shared_ptr< discretization > &d=ext::shared_ptr< discretization >(new EulerDiscretization), bool forceDiscretization=false)
Public Member Functions inherited from GeneralizedBlackScholesProcess
	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)
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
void	update () override
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 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 ()

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

Black-Scholes (1973) stochastic process.

This class describes the stochastic process \( S \) for a stock given by

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

Warning

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