QuantLib
A free/open-source library for quantitative finance
Reference manual - version 1.8
Public Member Functions | List of all members
GeneralizedBlackScholesProcess Class Reference

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 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
 
1-D stochastic process interface
- 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 &)
 
Observeroperator= (const Observer &)
 
std::pair< iterator, bool > registerWith (const boost::shared_ptr< Observable > &)
 
void registerWithObservables (const boost::shared_ptr< Observer > &)
 
Size unregisterWith (const boost::shared_ptr< Observable > &)
 
void unregisterWithAll ()
 
- Public Member Functions inherited from Observable
 Observable (const Observable &)
 
Observableoperator= (const Observable &)
 
void notifyObservers ()
 

Additional Inherited Members

- Public Types inherited from Observer
typedef std::set< boost::shared_ptr< Observable > > set_type
 
typedef set_type::iterator iterator
 
- Protected Member Functions inherited from StochasticProcess1D
 StochasticProcess1D (const boost::shared_ptr< discretization > &)
 
- Protected Member Functions inherited from StochasticProcess
 StochasticProcess (const boost::shared_ptr< discretization > &)
 
- Protected Attributes inherited from StochasticProcess1D
boost::shared_ptr< discretizationdiscretization_
 
- Protected Attributes inherited from StochasticProcess
boost::shared_ptr< discretizationdiscretization_
 

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

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.