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A Generalized Extreme Value Approach to Financial Risk Measurement

Authors


  • I thank the editor (Deborah Lucas) and an anonymous referee for their extremely helpful comments and suggestions. I also thank Geoffrey Booth, Peter Christoffersen, Haim Levy, Salih Neftci, Robert Schwartz, and Panayiotis Theodossiou for their useful comments and suggestions on earlier version of this article. I benefited from discussions with Linda Allen, Ozgur Demirtas, Armen Hovakimian, John Merrick, Lin Peng, and Liuren Wu on certain theoretical and empirical points. An earlier version of this paper was presented at the 2004 Econometric Society Meeting, Baruch College and the Graduate School and University Center of the City University of New York. I gratefully acknowledge the financial support from the Eugene Lang Research Foundation of the Zicklin School of Business, Baruch College, and the PSC-CUNY Research Foundation of the City University of New York.

Abstract

This paper develops an unconditional and conditional extreme value approach to calculating value at risk (VaR), and shows that the maximum likely loss of financial institutions can be more accurately estimated using the statistical theory of extremes. The new approach is based on the distribution of extreme returns instead of the distribution of all returns and provides good predictions of catastrophic market risks. Both the in-sample and out-of-sample performance results indicate that the Box–Cox generalized extreme value distribution introduced in the paper performs surprisingly well in capturing both the rate of occurrence and the extent of extreme events in financial markets. The new approach yields more precise VaR estimates than the normal and skewed t distributions.

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