Combining operational loss data with expert opinions through advanced credibility theory

ABSTRACT Working within the example of an extreme value theory-based loss distribution approach, we propose a model for integrating the historical operational value-at-risk (VaR), obtained by loss data analysis, and the prospective operational VaR, obtained by the analysis of experts' estimations, using a technique based on advanced credibility theory. The integration is performed at the level of frequency and severity distribution parameters. Among severity parameters, the primary role is played by the shape parameter of the severity tail distribution, which perceptibly affects the final capital figure. The proposed integration model allows us to obtain an integrated parameter estimation driven by the historical loss events and corrected using the information coming from expert opinions. The parameter integration is obtained by considering a compounded average of historical and subjective parameter estimate whose weights express the credibility assigned to each source and are provided by the Bühlmann- Straub model for advanced credibility theory.