The structural modeling of operational risk via Bayesian inference: combining loss data with expert opinions

To meet the Basel II regulatory requirements for the advanced measurement approaches, the bank's internal model must include the use of internal data, relevant external data, scenario analysis and factors reflecting the business environment and internal control systems. Quantification of operational risk cannot be based on historical data alone but should involve scenario analysis. Historical internal operational risk loss data has limited the ability to predict future behavior and, moreover, banks do not have enough internal data to estimate low-frequency, high-impact events adequately. Historical external data is difficult to use owing to different volumes and other factors. In addition, internal and external data have a survival bias, since typically one does not have data of all collapsed companies. The idea of scenario analysis is to estimate frequency and severity of risk events via expert opinions, taking into account bank environment factors with reference to events that have occurred (or may have occurred) in other banks. Scenario analysis is forward looking and can reflect changes in the banking environment. It is important to not only quantify the operational risk capital but also provide incentives to business units to improve their risk management policies, which can be accomplished through scenario analysis. By itself, scenario analysis is very subjective but combined with loss data it is a powerful tool for the estimation of operational risk losses. Bayesian inference is a statistical technique well suited for combining expert opinions and historical data. In this paper, we present examples of the Bayesian inference methods for operational risk quantification.