QuantLib
A free/open-source library for quantitative finance
Reference manual - version 1.5
Public Member Functions | List of all members
BlackScholesMertonProcess Class Reference

Merton (1973) extension to the Black-Scholes stochastic process. More...

#include <ql/processes/blackscholesprocess.hpp>

+ Inheritance diagram for BlackScholesMertonProcess:

Public Member Functions

 BlackScholesMertonProcess (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))
 
- Public Member Functions inherited from GeneralizedBlackScholesProcess
 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
 
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 evolve (Time t0, Real x0, Time dt, Real dw) const
 
void update ()
 
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 StochasticProcess1D
virtual Real stdDeviation (Time t0, Real x0, Time dt) const
 
virtual Real variance (Time t0, Real x0, Time dt) const
 
- 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< std::set
< boost::shared_ptr
< Observable > >::iterator,
bool > 
registerWith (const boost::shared_ptr< Observable > &)
 
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

- 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

Merton (1973) extension to the Black-Scholes stochastic process.

This class describes the stochastic process for a stock or stock index paying a continuous dividend yield given by

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

Examples:
ConvertibleBonds.cpp, DiscreteHedging.cpp, and EquityOption.cpp.