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Multivariate Estimation for Operational Risk with Judicious Use of Extreme Value Theory
Year Of Publication: 2006
Month Of Publication: November
Pages: 40
Download Count: 277
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Comment Num: 0
Language: EN
Source:
Who Can Read: Free
Date: 7-25-2007
Publisher: Administrator
Summary
The Basel II Accord requires participating banks to quantify operational risk accordingto a matrix of business lines and event types. Proper modeling of univariate lossdistributions and dependence structures across those categories of operational lossesis critical for proper assessment of overall annual operational loss distributions. Weillustrate our proposed methodology using Loss Data Collection Exercise 2004 (LDCE2004) data on operational losses across five loss event types. We estimate a multivariatelikelihood-based statistical model, which illustrates the benefits and risks ofusing extreme value theory (EVT) in modeling univariate tails of event type loss distributions.We find that abandoning EVT leads to unacceptably low estimates of riskcapital requirements, while indiscriminate use of EVT to all data leads to unacceptablyhigh ones. The judicious middle approach is to use EVT where dictated by data, andafter separating clear outliers that need to be modeled via probabilistic scenario analysis.We illustrate all computational steps in estimation of marginal distributions andcopula with an application to one bank’s data (disguising magnitudes to ensure thatbank’s anonymity). The methods we use to overcome heretofore unexplored technicalproblems in estimation of codependence across risk types scales easily to larger models,encompassing not only operational, but also other types of risk
Author(s)
El-Gamal, Mahmoud Sign in to follow this author
Inanoglu, Hulusi Sign in to follow this author
Stengel, Mitch Sign in to follow this author
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