Estimation of operational value-at-risk in the presence of minimum collection threshold: An empirical study

The recently finalized Basel II Capital Accord requires banks to adopt a procedure to estimate the operational risk capital charge. Under the Advanced Measurement Approaches, that are currently mandated for all large internationally active US banks, require the use of historic operational loss data. Operational loss databases are typically subject to a minimum recording threshold of roughly $10,000. We demonstrate that ignoring such thresholds leads to biases in corresponding parameter estimates when the threshold is ignored. Using publicly available operational loss data, we analyze the effects of model misspecification on resulting expected loss, Value-at-Risk, and Conditional Value-at-Risk figures and show that underestimation of the regulatory capital is a consequence of such model error. The choice of an adequate loss distribution is conducted via in-sample goodness-of-fit procedures and backtesting, using both classical and robust methodologies. ∗Department of Finance, M.J. Whitman School of Management, Syracuse University, NY 13244, USA. †School of Operations Research and Industrial Engineering, Cornell University, Ithaca, NY 14853, USA (this must be updated) ‡Institut für Statistik und Mathematische Wirtschaftstheorie, Universität Karlsruhe, Kollegium am Schloss, D76128 Karlsruhe, Germany, and Department of Statistics and Applied Probability, University of California at Santa Barbara, CA 93106, USA. Rachev gratefully acknowledges research support by grants from Division of Mathematical, Life and Physical Sciences, College of Letters and Science, University of California, Santa Barbara, the Deutschen Forschungsgemeinschaft and the Deutscher Akademischer Austausch Dienst. §Department of Business and Economics, Macquarie University, Sydney, NSW 2109, Australia 1