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).Comment: There are 32 pages, including tables, figures, appendix and
reference. The research was presented at the MATLAB Annual Computational
Finance Conference, September 27-30, 202