Evidence, estimates and extreme values from Austria

Stefan Kerbl

Abstract

ABSTRACT

We explore a new data source of operational loss events, the Austrian Loss Data Collection, featuring more than 42 000 observations. We provide statistical characteristics per event type and business line and analyze the cross-time and crosssection of the data. Subsequently, we make use of the data to address a central question of operational risk research: which approach is best suited to model the severity distribution of a single loss? Scientific attention to this question resulted in three major candidates: the generalized Pareto distribution (GPD), the central distribution of extreme value theory; the g-and-h distribution, an exotic relative to the lognormal; and the recently proposed semiparametric approach based on the modified Champernowne transformation. To evaluate the performance of each approach, we apply cross-validation. First, we find that capital requirements for operational risk are the best proxy for total losses of banks (among the considered indicators) and that, while frequency is highly correlated with size, mean losses are not. Second, we confirm the results of prior research that the GPD provides a very good fit in the cross-validation exercise. Additionally, the g-and-h distribution was found to rank second.