Heavy-tailed distributional model for operational losses

We examine the statistical properties of operational losses obtained from a large European bank using an actuarial-type framework. The simplistic assumption of a Poisson frequency distribution fails and we show that the frequency process follows closely a non-homogeneous Poisson process with a deterministic intensity of the form of a continuous cdf-like function. Further, operational losses are modeled using a variety of distributions. We address the problems of (1) reporting bias; (2) supplementing internal data with external data; (3) tail estimation; and (4) mixing the distributions of the body and the tail, and propose practical solutions to such problems. Finally, our empirical findings are consistent with other studies reporting very heavy-tailed loss distributions with the tail index below unity.