A COMPARISON OF SOME UNIVARIATE MODELS FOR VALUE-AT-RISK AND EXPECTED SHORTFALL

Carlo Marinelli (), Stefano d'Addona and Svetlozar T. Rachev ()
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Carlo Marinelli: Institut für Angewandte Mathematik, Universität Bonn, Wegelerstr. 6, D-53115 Bonn, Germany
Svetlozar T. Rachev: School of Economics and Business Engineering, University of Karlsruhe, Kollegium am Schloss, Bau II, 20.12, R210 D-76128 Karlsruhe, Germany; Department of Statistics and Applied Probability, University of California, Santa Barbara, CA 93106, USA

International Journal of Theoretical and Applied Finance (IJTAF), 2007, vol. 10, issue 06, pages 1043-1075

Abstract: We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α–stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

Keywords: Value-at-Risk; expected shortfall; Paretian stable laws; extreme value theory (search for similar items in EconPapers)
Date: 2007

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