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
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
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