Heavy-tailed distributional model for operational losses

We examine 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 a form of a continuous cdf-like function. Further, operational losses are modelled using variety of distributions. We address the problems of (1) reporting bias, (2) supplementing internal data with external, (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.