The Generalized Hyperbolic Distribution

The main topics covered in this chapter are:the definition and the main properties of the class of generalized hyperbolic distributions including different parameterizations, tail behavior, and central and non-central moments common in applications in finance;special subclasses which represent popular models in finance including the hyperbolic, the normal inverse Gaussian, the hyperbolic skewed t, the variance gamma, and other distributions;a random number generator for the general case and the most important subclasses;the method of maximum likelihood for parameter estimation for the general case and the most important subclasses;an empirical comparison of the fits of the generalized hyperbolic class and the most important subclasses based on the daily returns of the SPthe intuition behind the multivariate generalized hyperbolic distribution.