The Return Distribution of the Variance Gamma Process

This Demonstration shows the graphs of the density function of the unit period of a variance gamma process (red) and a Brownian motion process with drift (green). The variance gamma process is a three-parameter stochastic process that generalizes Brownian motion and was developed as a model for the dynamics of log stock prices. The process can be constructed as a Brownian motion with drift evaluated at random times given by a gamma process. The process thus has three parameters: the drift and volatility of the Brownian motion and the volatility of the gamma time change. Together they make it possible to control the skewness and kurtosis of the return distribution, which makes it possible to correct for the well-known biases of the Black–Scholes model (based on Brownian motion).