Operational loss scaling by exposure indicators: evidence from the ORX database

We investigate whether the size of operational risk losses can be correlated with geographical region and firm size. We extend past studies of losses on firm size by applying quantile regression techniques to obtain a more complete view of scaling relationships across the loss distribution. Furthermore, we test whether these distributional scaling relations can be described using simple location-shift or location-scale shift models. In addition, we develop a novel "quantile matching" algorithm to address statistical issues that arise when estimating loss scaling models when the data are subjected to a loss reporting threshold.