Multivariate estimation for operational risk with judicious use of extreme value theory

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 a proper assessment of overall annual operational loss distributions. We illustrate our proposed tnethodology 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 estimates. 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 of the computational steps in the 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 the estimation of codependence across risk types scales easily to larger models, encompassing not only operational, but also other types of risk.