Bayesian operational risk models

Operational risk is hard to quantify, for 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 risk assessment questionnaires, if properly modelled, may provide the missing piece of information that is necessary to adequately estimate op- erational risks. In this paper we propose to embody self risk assessment data into suitable prior distributions, and to follow a Bayesian approach to merge self assessment with loss data. We derive operational loss posterior distribu- tions, from which appropriate measures of risk, such as the Value at Risk, or the Expected Shortfall, can be derived. We test our proposed models on a real database, made up of internal loss data and self risk assessment questionnaires of an anonymous commercial bank. Our results show that the proposed Bayesian models performs better with respect to classical extreme value models, leading to a smaller quantification of the Value at Risk required to cover unexpected losses.