Modeling Very Large Losses. Ii

Abstract

This paper is a follow-up to the author’s 2018 paper in The Journal of Operational Risk (Volume 13, Issue 2, pages 83–91), the underlying idea of which was that very large operational risk losses should be aggregated to standard losses as a model extension. The latter are the losses described by risk type and business line in the Bank for International Settlements (BIS) classification, observed and duly recorded. A very large loss, when observed, might fit into one of the cells of the BIS classification, but we would not consider that it is caused by the same risk factors as the other losses in that cell. A pending detail in that paper is how to estimate the frequency of very large losses. Here we propose an approach to estimate very large losses similar to that used by Fermi and Drake to estimate the existence of extraterrestrial life. It consists of supposing the event of interest is the result of a concatenation of independent factors and estimating the probability of each factor. The problem is that the events in the causal chain might be events that have never been observed, which ties our subject to that of the estimation of probabilities of rare events. The other issue we address is how to take into account the existence of outliers in the standard losses. These outliers might be comparable with very large losses and have frequencies of occurrence similar to those of rare events. This must be taken into account when computing the value-at-risk of the full loss distribution.

Keywords: very large loss models, probability of a large loss, rare events, outliers, value-at-risk, expected shortfall