Variance gamma process. More...
#include <ql/experimental/variancegamma/variancegammaprocess.hpp>
Public Member Functions | |
| VarianceGammaProcess (Handle< Quote > s0, Handle< YieldTermStructure > dividendYield, Handle< YieldTermStructure > riskFreeRate, Real sigma, Real nu, Real theta) | |
| Real | x0 () const override |
| returns the initial value of the state variable | |
| 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 | sigma () const |
| Real | nu () const |
| Real | theta () const |
| const Handle< Quote > & | s0 () const |
| const Handle< YieldTermStructure > & | dividendYield () const |
| const Handle< YieldTermStructure > & | riskFreeRate () const |
| virtual Real | expectation (Time t0, Real x0, Time dt) const |
| virtual Real | stdDeviation (Time t0, Real x0, Time dt) const |
| virtual Real | variance (Time t0, Real x0, Time dt) const |
| virtual Real | evolve (Time t0, Real x0, Time dt, Real dw) const |
| virtual Real | apply (Real x0, Real dx) const |
| Public Member Functions inherited from StochasticProcess | |
| virtual Size | factors () const |
| returns the number of independent factors of the process | |
| virtual Time | time (const Date &) const |
| 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 | |
| Public Types inherited from Observer | |
| typedef set_type::iterator | iterator |
| StochasticProcess1D (ext::shared_ptr< discretization >) | |
| StochasticProcess (ext::shared_ptr< discretization >) | |
| ext::shared_ptr< discretization > | discretization_ |
| ext::shared_ptr< discretization > | discretization_ |
Detailed Description
Variance gamma process.
This class describes the stochastic volatility process. With a Brownian motion given by
\[ db = \theta dt + \sigma dW_t \]
then a Variance Gamma process X is defined by evaluating this Brownian motion at sample times driven by a Gamma process. If T is the value of a Gamma process with mean 1 and variance rate \( \nu \) then the Variance Gamma process is given by
\[ X(t) = B(T) \]
Member Function Documentation
◆ x0()
|
overridevirtual |
returns the initial value of the state variable
Implements StochasticProcess1D.
◆ 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.
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