  According to the Loss Distribution Approach, the operational risk of a bank
is determined as 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 by a Generalized Pareto Distribution (GPD).
Estimation of GPD tail quantiles is not a trivial task, in particular if one
takes 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. Moreover, if, as is frequently the case, operational losses
are pooled anonymously, relevance of the fitting data for the respective bank
is not self-evident. In such situations, robust methods may provide stable
estimates when classical methods already fail. In this paper, optimally-robust
procedures MBRE, OMSE, RMXE are introduced to the application domain of
operational risk. We apply these procedures to parameter estimation of a GPD at
data from Algorithmics Inc. To better understand these results, we provide
supportive diagnostic plots adjusted for this context: influence plots,
outlyingness plots, and QQ plots with robust confidence bands.
