Operational Risk Capital Modeling for Extreme Loss Events

Operational risk modeling using the parametric models can lead to a counterintuitive estimate of value at risk at 99.9% as economic capital due to extreme events. To address this issue, a flexible semi-nonparametric (SNP) model is introduced using the change of variables technique to enrich the family of distributions that can be used for modeling extreme events. The SNP models are proven to have the same maximum domain of attraction (MDA) as the parametric kernels, and it follows that the SNP models are consistent with the extreme value theory and peaks over threshold method, but with different shape and scale parameters. By using the simulated data sets generated from a mixture of distributions with varying body-tail thresholds, the SNP models in the Fréchet and Gumbel MDAs fit the data sets by increasing the number of model parameters, resulting in similar quantile estimates at 99.9%. When applied to an actual operational risk loss data set from a major international bank, the SNP models yield economic capital estimates 2 to 2.5 times as large as the single largest loss event and exhibit a reasonable stability towards the change of loss history in the scenario analysis.