A comparison of alternative mixing models for external data in operational risk

ABSTRACT When measuring its operational value-at-risk, a bank needs to pay attention when including external data in its analysis. Without careful consideration of the specific nature of the bank's risk there can be relevant systemic risk implications as pointed out by Torresetti and Nordio. Based on real operational risk data, we study alternative mixing models for external data for a particular risk class and show how scaling through a proxy for size for this risk class, as done by Shih, Samad-Khan and Medapa, does not seem to be a sensible technique for incorporating external data. Moving to more sophisticated mixing models, we show how kernel-modified estimators and Bayesian estimators represent an improvement. We also show how the technique outlined by Torresetti and Nordio is capable of further improving the treatment of external data in those instances where the case can be made for a distinct power law governing the tails of the internal and external data.