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

A comparison of extreme value theory approaches for determining value at risk
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 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.
bootstrap, value at risk (VaR), generalised pareto distribution, parametric, semi-nonparametric and small sample bias corrected tail index estimators, GARCH models
0927-5398
339-352
Brooks, C.
91d99e42-37f5-4b2b-87a2-c3df0c926b5f
Clare, A.D.
e9a9923a-dee5-4521-a5e1-d404befa7069
Dalle Molle, J.W.
fc5bbb2c-b7b0-47c7-a471-fbdf5497bee4
Persand, G.
c1b50342-bfb4-4a40-9f03-b352ba2076f2
Brooks, C.
91d99e42-37f5-4b2b-87a2-c3df0c926b5f
Clare, A.D.
e9a9923a-dee5-4521-a5e1-d404befa7069
Dalle Molle, J.W.
fc5bbb2c-b7b0-47c7-a471-fbdf5497bee4
Persand, G.
c1b50342-bfb4-4a40-9f03-b352ba2076f2

Brooks, C., Clare, A.D., Dalle Molle, J.W. and Persand, G. (2005) A comparison of extreme value theory approaches for determining value at risk. Journal of Empirical Finance, 12 (2), 339-352. (doi:10.1016/j.jempfin.2004.01.004).

Record type: Article

Abstract

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.

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Published date: 2005
Keywords: bootstrap, value at risk (VaR), generalised pareto distribution, parametric, semi-nonparametric and small sample bias corrected tail index estimators, GARCH models

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Local EPrints ID: 36527
URI: http://eprints.soton.ac.uk/id/eprint/36527
ISSN: 0927-5398
PURE UUID: 362b7103-415d-47bd-881f-9df8bf5f9cda

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Date deposited: 22 May 2006
Last modified: 15 Jul 2019 19:04

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Contributors

Author: C. Brooks
Author: A.D. Clare
Author: J.W. Dalle Molle
Author: G. Persand

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