Semi-nonparametric Estimation of Operational Risk Capital with Extreme Loss Events

Bank operational risk capital modeling using the Basel II advanced measurement approach (AMA) often lead to a counter-intuitive capital estimate of value at risk at 99.9% due to extreme loss 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 to handle extreme loss events. The SNP models are proved 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 peaks over threshold method but with different shape and scale parameters from the kernels. By using the simulation dataset generated from a mixture of distributions with both light and heavy tails, the SNP models in the Frechet and Gumbel MDAs are shown to fit the tail dataset satisfactorily through increasing the number of model parameters. The SNP model quantile estimates at 99.9 percent are not overly sensitive towards the body-tail threshold change, which is in sharp contrast to the parametric models. When applied to a bank operational risk dataset with three Basel event types, the SNP model provides a significant improvement in the goodness of fit to the two event types with heavy tails, yielding an intuitive capital estimate that is in the same magnitude as the event type total loss. Since the third event type does not have a heavy tail, the parametric model yields an intuitive capital estimate, and the SNP model cannot provide additional improvement. This research suggests that the SNP model may enable banks to continue with the AMA or its partial use to obtain an intuitive operational risk capital estimate when the simple non-model based Basic Indicator Approach or Standardized Approach are not suitable per Basel Committee Banking Supervision OPE10 (2019).