Conduct Risk - Distribution Models with Very Thin Tails

Abstract

Regulatory requirements dictate that financial institutions must calculate risk capital (funds that must be retained to cover future losses) at least annually. Procedures for doing this have been well-established for many years, but recent developments in the treatment of conduct risk (the risk of loss due to the relationship between a financial institution and its customers) have cast doubt on ‘standard’ procedures. Regulations require that operational risk losses should be aggregated by originating event. The effect is that a large number of small and medium-sized losses are aggregated into a small number of very large losses, such that a risk capital calculation produces a hugely inflated result. To solve this problem, a novel distribution based on a probability density with an exp(-x4/(2s2)) component is proposed, where s is a parameter to be estimated. Symbolic computation is used to derive the necessary analytical expressions with which to formulate the problem, and is followed by numeric calculations in R. Goodness-of-fit and parameter estimation are both determined by using a novel method developed specifically for use with probability distribution functions. The results compare favourably with an existing model that used a LogGamma Mixture density, for which it was necessary to limit the frequency and severity of the losses. No such limits were needed using the exp(-x4/2) density.