Modeling Operational Loss Severity Distributions from Consortium Data

ABSTRACT We describe a statistical methodology for identifying and characterizing the universe of loss severity distributions in a consortium loss database, using as few distributional models as possible. The procedure is based on successively clustering and pooling losses of various types according to different observed degrees of distributional homogeneity. We allow for the possibility of scaling loss data according to a simple linear transformation in order to bring the distribution into alignment.We address various estimation challenges in dealing with operational risk data, including handling issues around data truncation, ensuring that the resulting severity models are accurate in the high quantile levels of the distributions, and integrating the severity models into the loss distribution approach framework for computing regulatory capital. Finally, we describe the results of applying this methodology to the Operational Riskdata eXchange (ORX) global loss database.