Variance gamma process. More...
#include <ql/experimental/variancegamma/variancegammaprocess.hpp>
 Inheritance diagram for VarianceGammaProcess:
 Inheritance diagram for VarianceGammaProcess:| Public Member Functions | |
| VarianceGammaProcess (const Handle< Quote > &s0, const Handle< YieldTermStructure > ÷ndYield, const Handle< YieldTermStructure > &riskFreeRate, Real sigma, Real nu, Real theta) | |
| Real | x0 () const | 
| returns the initial value of the state variable | |
| Real | drift (Time t, Real x) const | 
| returns the drift part of the equation, i.e. \( \mu(t, x_t) \) | |
| Real | diffusion (Time t, Real x) const | 
| 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 | 
|  Public Member Functions inherited from StochasticProcess1D | |
| 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 () | 
|  Public Member Functions inherited from Observer | |
| Observer (const Observer &) | |
| Observer & | operator= (const Observer &) | 
| std::pair< iterator, bool > | registerWith (const boost::shared_ptr< Observable > &) | 
| void | registerWithObservables (const boost::shared_ptr< Observer > &) | 
| Size | unregisterWith (const boost::shared_ptr< Observable > &) | 
| void | unregisterWithAll () | 
| virtual void | deepUpdate () | 
|  Public Member Functions inherited from Observable | |
| Observable (const Observable &) | |
| Observable & | operator= (const Observable &) | 
| void | notifyObservers () | 
| Additional Inherited Members | |
|  Public Types inherited from Observer | |
| typedef std::set< boost::shared_ptr< Observable > > | set_type | 
| typedef set_type::iterator | iterator | 
|  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< discretization > | discretization_ | 
|  Protected Attributes inherited from StochasticProcess | |
| boost::shared_ptr< discretization > | discretization_ | 
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
\[ X(t) = B(T) \]