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Multivariate Models for Operational Risk: A Copula Approach using Extreme Value Theory and Poisson Shock Models

OPERATIONAL RISK TOWARD BASEL III: BEST PRACTICES AND ISSUES IN MODELING, MANAGEMENT, AND REGULATION, Wiley, pp. 197-218, March 2009

Posted: 3 Dec 2008 Last revised: 23 Dec 2011

Omar Rachedi

Universidad Carlos III de Madrid

Dean Fantazzini

Moscow School of Economics, Moscow State University; National Research University Higher School of Economics

Abstract

The aggregation of event types (ETs) is a crucial step for operational risk management techniques. Basel II requires the computation of a 99.9% VaR for each ET, and their aggregation via a simple sum if the dependence among ETs is not specified. Such a procedure assumes perfect positive dependence and therefore involves the implementation of the most conservative aggregation model. We propose a methodology that uses extreme-value theory to model the loss severities, copulas to model their dependence and a general Poisson shock model to capture the dependencies among ETs. We show that this approach allows the allocation of capital and hedge operational risk in a more efficient way than the standard approach.

Keywords: Copula, Extreme Value Theory, Losses Frequency , Losses Severity, Operational Risk, Shock model, VaR

JEL Classification: C15, C32, C51, G32

Suggested Citation

Rachedi, Omar and Fantazzini, Dean, Multivariate Models for Operational Risk: A Copula Approach using Extreme Value Theory and Poisson Shock Models. OPERATIONAL RISK TOWARD BASEL III: BEST PRACTICES AND ISSUES IN MODELING, MANAGEMENT, AND REGULATION, Wiley, pp. 197-218, March 2009. Available at SSRN: https://ssrn.com/abstract=1310642

Omar Rachedi

Universidad Carlos III de Madrid ( email )

CL. de Madrid 126
Madrid, Madrid 28903
Spain

Dean Fantazzini (Contact Author)

Moscow School of Economics, Moscow State University ( email )

GSP-2, Leninskie Gory
Moscow, 119992
Russia
+7 495 5105256 (Phone)
+7 495 5105267 (Fax)

HOME PAGE: https://sites.google.com/site/deanfantazzini/

National Research University Higher School of Economics ( email )

Myasnitskaya street, 20
Moscow, Moscow 119017
Russia

HOME PAGE: http://www.hse.ru/org/persons/11532644

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