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Journal of Financial Econometrics Advance Access originally published online on January 26, 2006
Journal of Financial Econometrics 2006 4(2):275-309; doi:10.1093/jjfinec/nbj006
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org.

The Generalized Hyperbolic Skew Student’s t-Distribution

Kjersti Aas
     Norwegian Computing Center

Ingrid Hobæk Haff
     Norwegian Computing Center

Address correspondence to Kjersti Aas, Norwegian Computing Center, Gaustadallen 23, P.O.Box 114, Blindern, NO-0314 Oslo, Norway, or e-mail: kjersti.aas{at}nr.no.

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.

KEYWORDS: EM algorithm, generalized hyperbolic distribution, NIG, skew probability distribution, skew Student’s t

Received March 10, 2005; revised August 11, 2005; accepted December 21, 2005


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