Estimation of Operational Value-at-Risk in the Presence of Minimum Collection Thresholds

The Basel II Capital Accord of 2004 sets guidelines on operational risk capital requirements to be adopted by internationally active banks by around year-end 2007. Operational loss databases are subject to a minimum recording threshold of roughly $10,000 (internal) and $1 million (external) – an aspect often overlooked by practitioners. We provide theoretical and empirical evidence that ignoring these thresholds leads to underestimation of the VaR and CVaR figures within the Loss Distribution Approach. We emphasize that four crucial components of a reliable operational loss actuarial model are: (1) non-homogenous Poisson process for the loss arrival process, (2) flexible loss severity distributions, (3) accounting for the incomplete data, and (4) robustness analysis of the model.