An efficient threshold choice for operational risk capital computation

Operational risk quantification requires dealing with data sets which often present extreme values which have a tremendous impact on capital computations (VaR). In order to take into account these effects we use extreme value distributions, and propose a two pattern model to characterize loss distribution functions associated to operational risks : a lognormal on the corpus of the severity distribution and a Generalized Pareto Distribution on the right tail. The threshold from which the model switches form a scheme to the other one is obtained using a bootstrap method. We use an extension of the Peak-over-threshold method to fit the GPD and the EM algorithm to estimate the lognormal distribution parameters. Through the VaR, we show the impact of the GPD estimation procedure on the capital requirements. Besides, our work points out the importance of the building's choice of the information set by practitioners to compute capital requirements and we exhibit some incoherences with the actual rules. Particularly, we highlight a problem arising from the granularity which has recently been mentioned by the Basel Committee for Banking Supervision.