ExtendedBlackScholesMertonProcess Class Reference
experimental Black-Scholes-Merton stochastic process More...
#include <ql/experimental/processes/extendedblackscholesprocess.hpp>
Inheritance diagram for ExtendedBlackScholesMertonProcess:
Public Types | |
| enum | Discretization { Euler , Milstein , PredictorCorrector } |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
Public Member Functions | |
| ExtendedBlackScholesMertonProcess (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), Discretization evolDisc=Milstein) | |
| Real | drift (Time t, Real x) const override |
| returns the drift part of the equation, i.e. \( \mu(t, x_t) \) | |
| Real | diffusion (Time t, Real x) const override |
| returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \) | |
| Real | evolve (Time t0, Real x0, Time dt, Real dw) const override |
| 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 | |
| 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 StochasticProcess | |
| virtual Size | factors () const |
| returns the number of independent factors of the process | |
| void | update () override |
| Public Member Functions inherited from Observer | |
| Observer (const Observer &) | |
| Observer & | operator= (const 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 | deepUpdate () |
| Public Member Functions inherited from Observable | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) |
| Observable (Observable &&)=delete | |
| Observable & | operator= (Observable &&)=delete |
| void | notifyObservers () |
Additional Inherited Members | |
| StochasticProcess1D (ext::shared_ptr< discretization >) | |
| StochasticProcess (ext::shared_ptr< discretization >) | |
| ext::shared_ptr< discretization > | discretization_ |
| ext::shared_ptr< discretization > | discretization_ |
Detailed Description
experimental Black-Scholes-Merton stochastic process
This class allows to choose a built-in discretization scheme
Member Function Documentation
◆ drift()
returns the drift part of the equation, i.e. \( \mu(t, x_t) \)
Implements StochasticProcess1D.
◆ diffusion()
returns the diffusion part of the equation, i.e. \( \sigma(t, x_t) \)
Implements StochasticProcess1D.
◆ evolve()
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.
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