Goodness-of-fit tests and selection methods for operational risk

ABSTRACT Within the loss distribution approach framework, the required capital is the 99.9% value-at-risk of the annual loss distribution, which is based on the fit of severity and frequency distributions using internal data. Supervisory guidelines for the advanced measurement approaches address the issue of the sensitivity of goodness-of-fit (GOF) tests to the sample size, the number of parameters estimated and the tail of the distributions. They suggest that a bank should consider selection methods that use the relative performance of the distributions at different confident levels. We investigate selection methods such as the Bayesian information criterion and the violation ratio as alternatives to the GOF tests. Attention is also paid to the main properties of the usual GOF tests performed in operational risks in order to determine the cases where the sensitivity raised by the guidelines is encountered and whether those tests could be reliable.