Operational Risk Quantification Using Extreme Value Theory and Copulas: From Theory to Practice

Journal of Operational Risk, 3 (2009), 1--24.

30 Pages Posted: 15 Jul 2008 Last revised: 27 Nov 2013

See all articles by Donato Abbate

Donato Abbate

Deloitte AG, Risk and Performance Management Group

Elise Gourier

ESSEC Business School

Walter Farkas

University of Zurich - Department of Banking and Finance; Swiss Finance Institute; ETH Zürich

Date Written: July 15, 2008

Abstract

In this paper we point out several pitfalls of the standard methodologies for quantifying operational losses. Firstly, we use Extreme Value Theory to model real heavy-tailed data. We show that using the Value-at-Risk as a risk measure may lead to a mis-estimation of the capital requirements. In particular, we examine the issues of stability and coherence and relate them to the degree of heavy-tailedness of the data. Secondly, we introduce dependence between the business lines using Copula Theory. We show that standard economic thinking about diversification may be inappropriate when infinite-mean distributions are involved.

Keywords: Extreme Value Theory, Copula Theory, Value-at-Risk, Sub-additivity, Coherence

Suggested Citation

Abbate, Donato and Gourier, Elise and Farkas, Walter, Operational Risk Quantification Using Extreme Value Theory and Copulas: From Theory to Practice (July 15, 2008). Journal of Operational Risk, 3 (2009), 1--24.. Available at SSRN: https://ssrn.com/abstract=1160167 or http://dx.doi.org/10.2139/ssrn.1160167

Donato Abbate

Deloitte AG, Risk and Performance Management Group ( email )

General Guisan-Quai 38
Zurich, 8022
Switzerland

Elise Gourier

ESSEC Business School ( email )

3 avenue Bernard Hirsch
Cergy-Pontoise, 95021
France

HOME PAGE: http://www.elisegourier.com

Walter Farkas (Contact Author)

University of Zurich - Department of Banking and Finance ( email )

Schönberggasse 1
Zürich, 8001
Switzerland
+41-44-634 3953 (Phone)
+41-44-634 4345 (Fax)

HOME PAGE: http://https://people.math.ethz.ch/~farkas/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

ETH Zürich ( email )

Rämistrasse 101
ZUE F7
Zürich, 8092
Switzerland

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