The Generalized Hyperbolic Skew Student's t-Distribution

Abstract

In this article we argue for a special case of the generalized hyperbolic (GH) family that we denote as the GH skew Student’s t-distribution. This distribution has the important property that one tail has polynomial and the other exponential behavior. Further, it is the only subclass of the GH family of distributions having this property. Although the GH skew Student’s t-distribution has been previously proposed in the literature, it is not well known, and specifically, its special tail behavior has not been addressed. This article presents empirical evidence of exponential/polynomial tail behavior in skew financial data, and demonstrates the superiority of the GH skew Student’s t-distribution with respect to data fit compared with some of its competitors. Through VaR and expected shortfall calculations we show why the exponential/polynomial tail behavior is important in practice.