The application of Extreme Value Theory in operational risk management

Abstract

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