A Scaling Model for Severity of Operational Losses Using Generalized Additive Models for Location Scale and Shape (GAMLSS)

In this paper, we investigate the problem of how to combine operational losses collected from various banks of different sizes and loss reporting thresholds in order to estimate the distribution of operational loss severities for a bank of a given size. We model the severity of operational losses by using the extreme value theory to account for the reporting bias of the external data, and a regression analysis based on the GAMLSS framework to model the scaling properties of operational losses. In contrast to previous studies on the scaling problem, our analysis give particular emphasis to the scaling properties of the tail of the loss distribution. Contrary to existing knowledge, we find that the size of a bank is an important determinant of the severity of operational losses and that the tail index of the distribution is negatively correlated with the size of the bank. The results indicate that for very large banks distribution of the operational loss severity can be extremely heavy tailed (i.e. tail index less than 1), a finding which have significant implications for capital calculation as well as for risk management. Furthermore, we also demonstrate the capital estimates provided by our model is consistent with the industry standards and the model can be used by individual banks to simulate data to complement their internal data