Risk Management with Generalized Hyperbolic Distributions

W. Hu and A. Kercheval (USA)

Keywords

Risk, VaR, Generalized Hyperbolic distributions, skewed t.

Abstract

We examine certain Generalized Hyperbolic (GH) distri butions for modeling equity returns, compared to usual Normal distributions. We describe these GH distributions and some of their properties, and test them against six years of daily S&P500 index prices. We estimate Value-at-Risk from calibrated distributions, and show that the Normal dis tribution leads to V aR estimates that signi´Čücantly underes timate the realized empirical values, while the GH distri butions do not. Of several GH distribution families con sidered, the most successful is the skewed-t distribution.

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