# The Normal Inverse Gaussian Lévy Process

The Normal Inverse Gaussian Lévy Process

This Demonstration shows a path of the normal inverse Gaussian (NIG) Lévy process and the graph of the probability density of the process at various moments in time. The NIG process is a pure-jump Lévy process with infinite variation, which has been used successfully in modeling the distribution of stock returns on the German and Danish exchanges. The version of the model shown here is controlled by three parameters that arise from the realization of the process as a time-changed Brownian motion with drift. The parameters are the drift and the volatility of the Brownian process and the variance of the (inverse Gaussian) subordinator (whose expectation is assumed to be 1). In the limiting case when the variance of the subordinator is set to zero, the NIG process coincides with Brownian motion and the probability density is normal. For other values of the variance, the NIG probability density has nonzero excess kurtosis and skewness, displayed beneath the graph on the right.

Note that a part of the path represented on the left may sometimes disappear from view, in which case one should adjust the "range of values" slider.