localVolatility (3) - Linux Manuals

localVolatility: Generalized Black-Scholes stochastic process.

Command to display localVolatility manual in Linux: $ man 3 localVolatility

NAME

QuantLib::GeneralizedBlackScholesProcess - Generalized Black-Scholes stochastic process.

SYNOPSIS

#include <ql/processes/blackscholesprocess.hpp>

Inherits QuantLib::StochasticProcess1D.

Inherited by BlackProcess, BlackScholesMertonProcess, BlackScholesProcess, ExtendedBlackScholesMertonProcess, and GarmanKohlagenProcess.

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

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

Detailed Description

Generalized Black-Scholes stochastic process.

This class describes the stochastic process governed by [ dS(t, S) = (r(t) - q(t) - ac{igma(t, S)^2}{2}) dt + igma dW_t. ]

Member Function Documentation

Real drift (Time t, Real x) const [virtual]

Possible enhancements

: revise extrapolation

Implements StochasticProcess1D.

Reimplemented in ExtendedBlackScholesMertonProcess.

Real diffusion (Time t, Real x) const [virtual]

Possible enhancements

: revise extrapolation

Implements StochasticProcess1D.

Reimplemented in ExtendedBlackScholesMertonProcess.

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.

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.

void update () [virtual]

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.