Merton (1973) extension to the Black-Scholes stochastic process. More...
#include <ql/processes/blackscholesprocess.hpp>
Public Member Functions | |
BlackScholesMertonProcess (const Handle< Quote > &x0, const Handle< YieldTermStructure > ÷ndTS, const Handle< YieldTermStructure > &riskFreeTS, const Handle< BlackVolTermStructure > &blackVolTS, const boost::shared_ptr< discretization > &d=boost::shared_ptr< discretization >(new EulerDiscretization)) | |
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GeneralizedBlackScholesProcess (const Handle< Quote > &x0, const Handle< YieldTermStructure > ÷ndTS, 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 |
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virtual Real | stdDeviation (Time t0, Real x0, Time dt) const |
virtual Real | variance (Time t0, Real x0, Time dt) const |
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virtual Size | factors () const |
returns the number of independent factors of the process | |
void | update () |
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Observer (const Observer &) | |
Observer & | operator= (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 () |
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Observable (const Observable &) | |
Observable & | operator= (const Observable &) |
void | notifyObservers () |
Additional Inherited Members | |
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StochasticProcess1D (const boost::shared_ptr< discretization > &) | |
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StochasticProcess (const boost::shared_ptr< discretization > &) | |
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boost::shared_ptr< discretization > | discretization_ |
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boost::shared_ptr< discretization > | discretization_ |
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
\[ dS(t, S) = (r(t) - q(t) - \frac{\sigma(t, S)^2}{2}) dt + \sigma dW_t. \]