Modeling operational risk data reported above a time-varying threshold

TL;DR

This paper develops methods for modeling operational risk data when the reporting threshold varies over time, incorporating both maximum likelihood and Bayesian approaches to improve loss distribution estimation.

Contribution

It introduces novel statistical techniques for fitting operational risk loss data with time-varying thresholds, addressing practical reporting policy changes.

Findings

Effective maximum likelihood estimation for variable thresholds

Bayesian MCMC methods for loss distribution fitting

Improved annual loss distribution estimation with parameter uncertainty

Abstract

Typically, operational risk losses are reported above a threshold. Fitting data reported above a constant threshold is a well known and studied problem. However, in practice, the losses are scaled for business and other factors before the fitting and thus the threshold is varying across the scaled data sample. A reporting level may also change when a bank changes its reporting policy. We present both the maximum likelihood and Bayesian Markov chain Monte Carlo approaches to fitting the frequency and severity loss distributions using data in the case of a time varying threshold. Estimation of the annual loss distribution accounting for parameter uncertainty is also presented.