A Bayesian approach to extreme value estimation in operational risk modeling

We propose a new approach for estimating operational risk models under the loss distribution approach from historically observed losses. Our method is based on extreme value theory and, being Bayesian in nature, allows us to incorporate other external information about the unknown parameters by use of expert opinions via elicitation or external data sources. This additional information can play a crucial role in reducing the statistical uncertainty about both parameter and capital estimates in situations where observed data are insufficient to accurately estimate the tail behavior of the loss distribution. Challenges of and strategies for formulating suitable priors are discussed. A simulation study demonstrates the performance of the new approach.