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 is a tail event. Supported by the Pickands-Balkema-de Haan Theorem, tail events exceeding some high threshold are usually modeled by a Generalized Pareto Distribution (GPD). However, because of the heavy-tailedness of this distribution, estimation of its tail quantiles is not a trivial task, which becomes even more difficult when there are outliers in the data, or data is pooled among several sources. In such situations where the origin and representativeness of the available data is not clear , robust methods provide a remedy which can provide reliable estimates when classical methods already fail. We illustrate this , applying such robust methods for parameter estimation of a GPD - including some recently developed methods - to data from Algorithmics Inc. To better understand these results, we provide some useful diagnostic plots adjusted for this context: influence plot, outlyingness plot , and QQ plot with robust confidence bands.
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.
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