The Application of Extreme Value Theory in Operational Risk Management

Abstract

This paper focuses on modeling the real operational data of an anonymousCentral European bank. We have applied the Extreme Value Theory, inwhich we have used two estimation methods - the standard maximumlikelihood estimation method and the probability weighted moments (PWM).Our results proved a heavy-tailed pattern of operational risk data asdocumented by many researchers. Additionally, we showed that the PWM isquite consistent when the data is limited as it was able to providereasonable and consistent capital estimates. Our findings show that whenusing the Advanced Measurement Approach rather than the Basic IndicatorApproach used in Basel II, the researched bank might save approx. 6-8%of its capital requirement on operational risk.