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The Quantitative Modeling of Operational Risk: Between G-and-H and EVT

Published online by Cambridge University Press:  17 April 2015

Matthias Degen ,
Paul Embrechts  and
Dominik D. Lambrigger
Matthias Degen
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
Paul Embrechts
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
Dominik D. Lambrigger
Affiliation:
Department of Mathematics, ETH Zurich, 8092 Zurich, Switzerland
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Abstract

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Operational risk has become an important risk component in the banking and insurance world. The availability of (few) reasonable data sets has given some authors the opportunity to analyze operational risk data and to propose different models for quantification. As proposed in Dutta and Perry [12], the parametric g-and-h distribution has recently emerged as an interesting candidate.

In our paper, we discuss some fundamental properties of the g-and-h distribution and their link to extreme value theory (EVT). We show that for the g-and-h distribution, convergence of the excess distribution to the generalized Pareto distribution (GPD) is extremely slow and therefore quantile estimation using EVT may lead to inaccurate results if data are well modeled by a g-and-h distribution. We further discuss the subadditivity property of Value-at-Risk (VaR) for g-and-h random variables and show that for reasonable g and h parameter values, superadditivity may appear when estimating high quantiles. Finally, we look at the g-and-h distribution in the one-claim-causes-ruin paradigm.

Keywords

Extreme Value Theoryg-and-h DistributionHill EstimatorLDAOperational RiskPeaks Over ThresholdSecond Order Regular VariationSubadditivityValue-at-Risk
Type
Articles
Information
ASTIN Bulletin: The Journal of the IAA , Volume 37 , Issue 2 , November 2007 , pp. 265 - 291
Copyright
Copyright © ASTIN Bulletin 2007

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