Article2007

Risk management with generalized hyperbolic distributions

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Statistical Distribution Estimation and Applications

Abstract

We examine certain Generalized Hyperbolic (GH) distributions 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 distribution leads to V aR estimates that significantly underestimate the realized empirical values, while the GH distributions do not. Of several GH distribution families considered, the most successful is the skewed-t distribution.

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References

1999Coherent Measures of Risk 1995Techniques for Verifying the Accuracy of Risk Measurement Models 2005Quantitative Risk Management: Concepts, Techniques, and Tools 2002Correlation and Dependence in Risk Management: Properties and Pitfalls 2007The t Copula and Related Copulas 1995Hyperbolic Distributions in Finance 2005Calibration of multivariate generalized hyperbolic distributions using the em algorithm, with applications in risk management, portfolio optimization and portfolio credit risk

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