Value-at-Risk Prediction by Higher Moment Dynamics

Abstract

In this paper the out-of-sample prediction of Value-at-Risk by means of models accounting for higher moment dynamics is studied. We consider models differing in terms of skewness and urtosis and, in particular, the GARCHDSK model, which allows for dynamic skewness and kurtosis. The issue of VaR prediction performance is approached first by a purely statistical viewpoint, studying the properties of correct coverage rates and independence of VaR violations. Then, financial implications of different VaR models, in terms of market risk capital requirements, as defined by the Basel Accord, are considered. Our results, based on the analysis of eight international stock indexes, highlight the presence of time-varying conditional skewness and kurtosis and point out that asymmetry plays a significant role in risk management.

Keywords: VaR prediction, GARCHDSK, dynamic skewness, dynamic kurtosis

JEL Classification: C2, C22