Semi-nonparametric estimation of operational risk capital with extreme loss events

Heng Z. Chen and Stephen R. Cosslett

Abstract

The Basel II advanced measurement approach often leads to a counterintuitive value-at- risk operational risk capital for regulatory requirements due to extreme loss events. To address this issue, this research suggests that the semi-nonparametric (SNP) model proposed in 1997 by Chen and Randall can be adopted to enrich the family of distributions for the parametric model misspecification. Further, the SNP model is shown to have the same maximum domain of attraction as its parametric kernel, and it follows that the SNP methodology is consistent with the extreme value theory–peak over threshold method but with shape and scale parameters that can be different than those of its parametric kernel. By using both actual and simulated operational risk loss data sets, the SNP model is shown to be a significant improvement on the parametric model and to capture heavy tails satisfactorily through an appropriate increase in the number of parameters. The SNP quantile estimates at 99.9% are not overly sensitive toward the change of body–tail thresholds anymore, which is in sharp contrast to the parametric model. The capital estimate becomes intuitive and is of the same magnitude as the total operational risk loss. These results suggest that the SNP model may enable banks to continue to use the advanced measurement approach (or part of it) to manage their operational risks with an intuitive, measurable and risk sensitive capital when the non-model-based basic indicator approach or standardized measurement approach is not suitable, as per the OPE10 definitions for the Basel Committee on Banking Supervision’s calculations of risk-weighted assets for operational risk.