QuantLib_GeneralizedBlackScholesProcess man page

GeneralizedBlackScholesProcess — Generalized Black-Scholes stochastic process.

Synopsis

#include <ql/processes/blackscholesprocess.hpp>

Inherits StochasticProcess1D.

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

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

Real variance (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

Additional Inherited Members

Detailed Description

Generalized Black-Scholes stochastic process.

This class describes the stochastic process $ S $ governed by [ dln S(t) = (r(t) - q(t) - ac{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

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

Implements StochasticProcess1D.

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

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

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.

Real stdDeviation (Time t0, Real x0, Time dt) const [virtual]

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.

Real variance (Time t0, Real x0, Time dt) const [virtual]

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.

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.

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.

Implements Observer.

Author

Generated automatically by Doxygen for QuantLib from the source code.

Referenced By

blackVolatility(3), GeneralizedBlackScholesProcess(3), localVolatility(3) and stateVariable(3) are aliases of QuantLib_GeneralizedBlackScholesProcess(3).

Fri Sep 23 2016 Version 1.8.1 QuantLib