Merton (1973) extension to the Black-Scholes stochastic process. More...
#include <blackscholesprocess.hpp>
Inheritance diagram for BlackScholesMertonProcess:
Collaboration diagram for BlackScholesMertonProcess:
Public Member Functions | |
| BlackScholesMertonProcess (const Handle< Quote > &x0, const Handle< YieldTermStructure > ÷ndTS, const Handle< YieldTermStructure > &riskFreeTS, const Handle< BlackVolTermStructure > &blackVolTS, const ext::shared_ptr< discretization > &d=ext::shared_ptr< discretization >(new EulerDiscretization), bool forceDiscretization=false) | |
| Public Member Functions inherited from GeneralizedBlackScholesProcess | |
| GeneralizedBlackScholesProcess (Handle< Quote > x0, Handle< YieldTermStructure > dividendTS, Handle< YieldTermStructure > riskFreeTS, Handle< BlackVolTermStructure > blackVolTS, const ext::shared_ptr< discretization > &d=ext::shared_ptr< discretization >(new EulerDiscretization), bool forceDiscretization=false) | |
| GeneralizedBlackScholesProcess (Handle< Quote > x0, Handle< YieldTermStructure > dividendTS, Handle< YieldTermStructure > riskFreeTS, Handle< BlackVolTermStructure > blackVolTS, Handle< LocalVolTermStructure > localVolTS) | |
| Real | x0 () const override |
| returns the initial value of the state variable More... | |
| Real | drift (Time t, Real x) const override |
| Real | diffusion (Time t, Real x) const override |
| Real | apply (Real x0, Real dx) const override |
| Real | expectation (Time t0, Real x0, Time dt) const override |
| Real | stdDeviation (Time t0, Real x0, Time dt) const override |
| Real | variance (Time t0, Real x0, Time dt) const override |
| Real | evolve (Time t0, Real x0, Time dt, Real dw) const override |
| Time | time (const Date &) const override |
| void | update () override |
| 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 | |
| Public Member Functions inherited from StochasticProcess | |
| ~StochasticProcess () override=default | |
| virtual Size | factors () const |
| returns the number of independent factors of the process More... | |
| void | update () override |
| Public Member Functions inherited from Observer | |
| Observer ()=default | |
| Observer (const Observer &) | |
| Observer & | operator= (const Observer &) |
| virtual | ~Observer () |
| std::pair< iterator, bool > | registerWith (const ext::shared_ptr< Observable > &) |
| void | registerWithObservables (const ext::shared_ptr< Observer > &) |
| Size | unregisterWith (const ext::shared_ptr< Observable > &) |
| void | unregisterWithAll () |
| virtual void | update ()=0 |
| virtual void | deepUpdate () |
| Public Member Functions inherited from Observable | |
| Observable () | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| Observable (Observable &&)=delete | |
| Observable & | operator= (Observable &&)=delete |
| virtual | ~Observable ()=default |
| void | notifyObservers () |
Additional Inherited Members | |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
| Protected Member Functions inherited from StochasticProcess1D | |
| StochasticProcess1D ()=default | |
| StochasticProcess1D (ext::shared_ptr< discretization >) | |
| Protected Member Functions inherited from StochasticProcess | |
| StochasticProcess ()=default | |
| StochasticProcess (ext::shared_ptr< discretization >) | |
| Protected Attributes inherited from StochasticProcess1D | |
| ext::shared_ptr< discretization > | discretization_ |
| Protected Attributes inherited from StochasticProcess | |
| ext::shared_ptr< discretization > | discretization_ |
Detailed Description
Merton (1973) extension to the Black-Scholes stochastic process.
This class describes the stochastic process ln(S) for a stock or stock index paying a continuous dividend yield given by
\[ d\ln S(t, S) = (r(t) - q(t) - \frac{\sigma(t, S)^2}{2}) dt + \sigma dW_t. \]
Definition at line 144 of file blackscholesprocess.hpp.
Constructor & Destructor Documentation
◆ BlackScholesMertonProcess()
| BlackScholesMertonProcess | ( | const Handle< Quote > & | x0, |
| const Handle< YieldTermStructure > & | dividendTS, | ||
| const Handle< YieldTermStructure > & | riskFreeTS, | ||
| const Handle< BlackVolTermStructure > & | blackVolTS, | ||
| const ext::shared_ptr< discretization > & | d = ext::shared_ptr<discretization>(new EulerDiscretization), |
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| bool | forceDiscretization = false |
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| ) |
Definition at line 245 of file blackscholesprocess.cpp.