Bayesian inference methods in operational risk

Sammanfattning: Under the Advanced Measurement Approach (AMA), banks must use four different sources of information to assess their operational risk capital requirement. The three main quantitative sources available to build the future loss distribution are internal loss data, external loss data and scenario analysis. The fourth source, business environment and internal control factors, is treated as an ex-post update to capital calculations and is not a subject of this thesis. Ap- proaches from Extreme Value Theory (EVT) have gained popularity in the area of operational risk in recent years, with its focus on the behaviour of processes at extreme levels making it a natural candidate for operational risk modelling. However, the adoption of EVT in operational risk modelling has encountered several obstacles with the main one being the scarcity of data leading to substantial statistical uncertainty for both parameter and capital estimates. This Master thesis evaluates Bayesian Inference approaches to extreme value estimation and implements a method to reduce these uncertainties. The results indicate that the Bayesian Inference approaches gives a significant reduction of the statistical uncertainties compared to more traditional estimators and also performs well when applied on real-world data sets.