Operational Risk Models and Asymptotic Normality of Maximum Likelihood Estimation

24 Pages Posted: 23 Nov 2016  

Paul Larsen

Allianz SE

Date Written: November 23, 2016

Abstract

Operational risk models commonly employ maximum likelihood estimation (MLE) to fit loss data to heavy-tailed distributions. Yet several desirable properties of MLE (e.g., asymptotic normality) are generally valid only for large sample sizes, a situation that is rarely encountered in operational risk. In this paper, we study how asymptotic normality does, or does not, hold for common severity distributions in operational risk models. We then apply these results to evaluate errors caused by failure of asymptotic normality in constructing confidence intervals around the MLE fitted parameters.

Keywords: asymptotic normality, heavy-tailed distributions, maximum likelihood estimation (MLE), operational risk models, loss distribution approach (LDA)

Suggested Citation

Larsen, Paul, Operational Risk Models and Asymptotic Normality of Maximum Likelihood Estimation (November 23, 2016). Journal of Operational Risk, Vol. 11, No. 4, 2016. Available at SSRN: https://ssrn.com/abstract=2874768

Paul Larsen (Contact Author)

Allianz SE ( email )

Königinstrasse 28
Munich, 80802
Germany

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