Robust estimation of operational risk

ABSTRACT According to the loss distribution approach, the operational risk of a bank is determined as the 99.9% quantile of the respective loss distribution, covering unexpected severe events. The 99.9% quantile can be considered a tail event. As supported by the Pickands-Balkema-de Haan theorem, tail events exceeding some high threshold are usually modeled using a generalized Pareto distribution (GPD). Estimation of GPD tail quantiles is not a trivial task, particularly if we take into account the heavy tails of this distribution, the possibility of singular outliers, and, moreover, the fact that data is usually pooled among several sources. In such situations, robust methods may provide stable estimates in situations where classical methods fail. In this paper, the optimally robust procedures "most bias-robust estimator", "optimal mean squared error estimator" and "radiusminimax estimator" are introduced to the application domain of operational risk. We apply these procedures to parameter estimation of a GPD from data from Algorithmics Inc. To better understand these results, supportive diagnostic plots adjusted for this context (influence plots, outlyingness plots and QQ plots with robust confidence bands) are provided.