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EVT-based estimation of risk capital and convergence of high quantiles

Part of: Nonparametric inference Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Matthias Degen  and
Paul Embrechts
Matthias Degen*
Affiliation:
ETH Zurich
Paul Embrechts*
Affiliation:
ETH Zurich
*
∗ Postal address: Department of Mathematics, ETH Zurich, Raemistrasse 101, CH-8092 Zurich, Switzerland.
∗ Postal address: Department of Mathematics, ETH Zurich, Raemistrasse 101, CH-8092 Zurich, Switzerland.
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Abstract

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We discuss some issues regarding the accuracy of a quantile-based estimation of risk capital. In this context, extreme value theory (EVT) emerges naturally. The paper sheds some further light on the ongoing discussion concerning the use of a semi-parametric approach like EVT and the use of specific parametric models such as the g-and-h. In particular, we discusses problems and pitfalls evolving from such parametric models when using EVT and highlight the importance of the underlying second-order tail behavior.

Keywords

Extreme value theoryg-and-h distributionoperational riskpeaks over thresholdpenultimate approximationsecond-order regular variationslow variationvalue at risk

MSC classification

Primary: 60G70: Extreme value theory; extremal processes
Secondary: 62G32: Statistics of extreme values; tail inference
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 40 , Issue 3 , September 2008 , pp. 696 - 715
Copyright
Copyright © Applied Probability Trust 2008 

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