Goodness-of-Fit Tests and Selection Methods for Operational Risk
Journal of Operational Risk 9(3), 21-50
30 Pages Posted: 23 May 2014 Last revised: 28 Mar 2015
Date Written: July 25, 2014
Within the Loss Distribution Approach (LDA) 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 to 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. In this paper, a study is conducted to investigate selection methods such as the Bayesian Information Criterion and the violation ratio as alternatives to the GOF tests. Attention is also given to the main properties of the usual GOF tests performed in operational risks in order to figure out the cases where the sensitivity raised by the guidelines is encountered and if those tests could be reliable though.
Keywords: Operational risk; Loss Distribution Approach; Goodness-of-fit tests; Schwarz Bayesian Criterion; violation ratio; Lognormal distribution; Truncated data
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