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

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