Operational Risk toward Basel III: Best Practices and Issues in Modeling, Management, and Regulation

CHAPTER 10

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

Omar Rachedi and Dean Fantazzini

 

 

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.

Omar Rachedi thanks Professor Carlo Bianchi, Dr. Giorgio Aprile, and Francesca Fabbri for their comments and suggestions.

10.1 INTRODUCTION

The quantitative analysis of operational risk is a relative recent field of study within the more general quantitative risk management framework (see King 2001 and Cruz 2002). The operational risk issue has arisen when both market risk management and credit risk management have been found unable to hedge all possible events affecting the economic and financial results of financial institutions.

The development of this subject is a direct consequence of the New Capital ...