A comparison of extreme value theory approaches for determining value at risk

This paper compares a number of different extreme value models for determining the value at risk (VaR) 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 captu...

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Bibliographic Details
Published in:Journal of empirical finance 2005-03, Vol.12 (2), p.339-352
Main Authors: Brooks, C., Clare, A.D., Dalle Molle, J.W., Persand, G.
Format: Article
Language:English
Subjects:
Bootstrap
Finance
GARCH models
Generalised Pareto Distribution
Parametric
Pareto efficiency
Regression analysis
Risk
Semi-nonparametric and small sample bias corrected tail index estimators
Value at risk (VaR)
Value theory
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Summary:This paper compares a number of different extreme value models for determining the value at risk (VaR) 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 holdout sample, the proposed semi-nonparametric extreme value approach yields superior results to other methods, but the small sample tail index technique is also accurate.
ISSN:0927-5398
1879-1727
DOI:10.1016/j.jempfin.2004.01.004