Publications:
Multivariate Estimation for Operational Risk with Judicious Use of Extreme Value Theory
by Mahmoud El-Gamal, Hulusi Inanoglu, and Mitch Stengel
Abstract: The Basel II Accord requires participating banks to quantify operational risk according
to a matrix of business lines and event types. Proper modeling of univariate loss
distributions and dependence structures across those categories of operational losses
is critical for proper assessment of overall annual operational loss distributions. We
illustrate our proposed methodology using Loss Data Collection Exercise 2004 (LDCE
2004) data on operational losses across five loss event types. We estimate a multivariate
likelihood-based statistical model, which illustrates the benefits and risks of
using extreme value theory (EVT) in modeling univariate tails of event type loss distributions.
We find that abandoning EVT leads to unacceptably low estimates of risk
capital requirements, while indiscriminate use of EVT to all data leads to unacceptably
high ones. The judicious middle approach is to use EVT where dictated by data, and
after separating clear outliers that need to be modeled via probabilistic scenario analysis.
We illustrate all computational steps in estimation of marginal distributions and
copula with an application to one bank's data (disguising magnitudes to ensure that
bank's anonymity). The methods we use to overcome heretofore unexplored technical
problems in estimation of codependence across risk types scales easily to larger models,
encompassing not only operational, but also other types of risks.
Disclaimer
Any whole or partial reproduction of material in this paper should include the following citation: Mahmoud El-Gamal, Hulusi Inanoglu, and Mitch Stengel, "Multivariate Estimation for Operational Risk with Judicious Use of Extreme Value Theory," Office of the Comptroller of the Currency, Economics Working Paper 2006-3, November 2006.
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