An efficient threshold choice for the computation of operational risk capital

ABSTRACT The quantification of operational risk often involves dealing with data sets that present extreme values, which have a tremendous impact on capital computations (value-at-risk). In order to take these effects into account we use extreme value distributions and propose a two-pattern model to characterize loss distribution functions associated with operational risks: a lognormal on the corpus of the severity distribution and a generalized Pareto distribution (GPD) on the right tail. The threshold at which the model switches from one scheme to the other is obtained using a bootstrap method.We use an extension of the peaks-over-threshold method to fit the GPD and the expectation-maximization algorithm to estimate the lognormal distribution parameters. Through the value-at-risk, we show the impact of the GPD estimation procedure on the capital requirements. Furthermore, our work points out the dramatic impact of the way practitioners construct their information sets on capital requirement computations, and we exhibit some incoherences with the actual rules. In particular, we highlight a problem arising from the granularity that has recently been mentioned by the Basel Committee for Banking Supervision.