"Estimation of Operational Value-at-Risk with Minimum Collection Thresholds"


Anna Chernobai (1), Stefan Trück (2) and Svetlozar T. Rachev (1,2)

(1) Department of Statistics and Applied Probability
    University of California, Santa Barbara, CA 93106, USA
(2) Institut für Statistik und Mathematische Wirtschaftstheorie
    Universität Karlsruhe, Kollegium am Schloss, D-76128 Karlsruhe, Germany


Abstract

Due to regulatory capital requirements scheduled to become effective by the end 
of 2006, financial institutions put substantial effort in collecting loss data 
and determining adequate loss distributions for operational risk types. However, 
thresholds in the collection of operational loss data lead to biased estimates 
as not all loss cases enter internal databases. We provide an approach to the 
estimation of left-truncated severity data using the EM-algorithm. We extend 
the model to adjust the frequency and the aggregated loss distributions, and 
quantify the impact on the Value-at-Risk figures. Furthermore, the paper 
demonstrates that the effects are more substantial for heavier-tailed 
distributions.