Fitting operational risk data using limited information below the threshold

Christopher M. Cormack

Abstract

ABSTRACT

This paper presents a methodology to calibrate the distribution of losses observed in operational risk events. The method is specifically designed to handle the situation where individual event information is only available above an approved threshold and there is a limited set of below-threshold information (BTI). The method requires the use of the number of events and the sum of the losses below the threshold. the authors demonstrate the improved stability of the fitted distribution parameters as the number of events above the threshold is reduced. This is compared with the conventional truncated maximum likelihood estimator (MLE). To demonstrate the improved stability of the parameter estimation using the BTI, a series of fits are performed to m samples of N events drawn from a lognormal distribution, and these are compared with estimates of the truncated MLE. The BTI fitting methodology produces a better estimator of the population distribution parameters, with reduced bias and dispersion. the authors estimate the 99.9th percentile of the severity distribution and show that the BTI provides a better estimator of the percentile with reduced uncertainty.