VarianceGammaProcess Class Reference

Variance gamma process. More...

#include <ql/experimental/variancegamma/variancegammaprocess.hpp>

Inheritance diagram for VarianceGammaProcess:

List of all members.

Public Member Functions

 VarianceGammaProcess (const Handle< Quote > &s0, const Handle< YieldTermStructure > &dividendYield, 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

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

\[ X(t) = B(T) \]