Title: Modelling multidimensional extremal dependance for operational risk
Authors: Claudia Klueppelberg - Technical University of Munich (Germany)
Sandra Paterlini - European Business School Germany (Germany) [presenting]
Oliver Key - Technical University Munich (Germany)
Abstract: A statistical model of operational losses is introduced based on extreme value distributions and bipartite graphs, which perfectly capture the event type and business line structure of operational risk data. The model explicitly takes into account the Pareto tails of losses as well as heterogeneous dependence structures between them. We then derive estimators for individual as well as aggregated tail risk, measured in terms of Value-at-Risk and Conditional Tail Expectations for very high confidence levels. Asymptotic properties as well as upper and lower bounds are discussed. We introduce then two estimation methods for such risk-measures and test their validity on simulated data. Finally, by having access to real-world operational risk losses from the Italian banking system, we show that the estimated quantities converge to the asymptotic values and show that quantifying dependence by means of the empirical severity and frequency distribution can have quite an impact on estimates at both individual and aggregate level.