On Modeling Operational Risk using Extreme Value Theory

Sammanfattning: The main goal of this thesis is to show how operational risk can be measured if even the use of standard extreme value theory fails to explain single catastrophic events in the tail of the distribution. Against the background of regulatory requirements imposed by the Basel Accords, an Advanced Measurement Approach (AMA) is developed for a dataset of operational losses occurred in US businesses between 1985 and 2008. Two alternative approaches are described for modeling the loss frequency when the losses are reported by the month. A copula approach is applied to capture dependence among dierent loss distributions corresponding to dierent event types. The resulting 99:9% Value-at-Risk, which determines the capital requirement, is compared to a model assuming perfect dependence.