Asyptotic Normality for Maximum Likelihood Estimation and Operational Risk

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 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.