Quantification of operational risk: statistical insights on coherent risk measures

Operational risk is becoming a major part of corporate governance in companies, especially in the financial services industry. In this paper, we review some of the existing methods used to quantify operational risks in the banking and insurance industries. These methods use recent statistical concepts such as extreme value theory and copula modeling. We explore the possibility of using a coherent risk measure - expected shortfall (ES) - to quantify operational risk. The suitability of the suggested risk measures has been investigated with the help of simulated data sets for two business lines. The generalized Pareto distribution is used for modeling the tails, and three distributions - lognormal, Weibull and Gamma - are used for the body data. Our results show that ES under all three distributions tends to be significantly larger than value-at-risk, which may lead to overestimating the operational loss and consequently overestimating the capital charge. However, the modified ES seems to provide a better way of mitigating any overestimation.