Bayesian operational risk models

ABSTRACT Operational risk is hard to quantify, due to the presence of heavy tailed loss distributions. Extreme value distributions, used in this context, are very sensitive to the data, and this is a problem in the presence of rare loss data. Self-assessment questionnaires for risk, if properly structured, may provide prior opinions that can be used, in a Bayesian analysis, to better estimate operational risks. In this paper we propose a methodology to frame risk self-assessment data into suitable prior distributions that, updated with the observed loss data, can produce posterior distributions from which accurate operational risk measures, such as value-at-risk (VaR), can be obtained. We test our proposed model on a real database, made up of internal loss data and risk self-assessment questionnaires of an anonymous commercial bank. Our results show that the proposed Bayesian models perform better with respect to classical extreme value models, leading to a smaller quantification of the VaR required to cover unexpected losses.