A Comparison of Extreme Value Theory Approaches for Determining Value at Risk

20 Pages Posted: 5 Dec 2004

See all articles by Chris Brooks

Chris Brooks

University of Reading - ICMA Centre

Andrew Clare

City University London - Sir John Cass Business School

John W. Dalle Molle

Independent

Gita Persand

University of Bristol - Department of Economics

Abstract

This paper compares a number of different extreme value models for determining the value at risk of three LIFFE futures contracts. A semi-nonparametric approach is also proposed where the tail events are modeled using the Generalised Pareto Distribution and normal market conditions are captured by the empirical distribution function. The value at risk estimates from this approach are compared with those of standard nonparametric extreme value tail estimation approaches, with a small sample bias-corrected extreme value approach, and with those calculated from bootstrapping the unconditional density and bootstrapping from a GARCH(1,1) model. The results indicate that for a hold-out sample, the proposed semi-nonparametric extreme value approach yields superior results to other methods, but the small sample tail index technique is also accurate.

Keywords: Bootstrap, Value at Risk (VaR), Generalised Pareto Distribution, Parametric, Semi-nonparametric and Small Sample Bias Corrected Tail Index Estimators, GARCH models

JEL Classification: C14, C15, G13

Suggested Citation

Brooks, Chris and Clare, Andrew D. and Dalle Molle, John W. and Persand, Gita, A Comparison of Extreme Value Theory Approaches for Determining Value at Risk. Journal of Empirical Finance, Forthcoming; Cass Business School Research Paper. Available at SSRN: https://ssrn.com/abstract=626682

Chris Brooks (Contact Author)

University of Reading - ICMA Centre ( email )

Whiteknights Park
P.O. Box 242
Reading RG6 6BA
United Kingdom
+44 118 931 82 39 (Phone)
+44 118 931 47 41 (Fax)

Andrew D. Clare

City University London - Sir John Cass Business School ( email )

106 Bunhill Row
London, EC1Y 8TZ
United Kingdom

John W. Dalle Molle

Independent ( email )

No Address Available

Gita Persand

University of Bristol - Department of Economics ( email )

8 Woodland Road
Bristol BS8 ITN
United Kingdom

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