Should risk managers rely on the maximum likelihood estimation method while quantifying operational risk?

Abstract

This paper compares the performance of four estimation methods, including the maximum likelihood estimation method, which can be used in fitting operational risk models to historically available loss data. The other competing methods are based on minimizing different types of measure for the distance between empirical and fitting loss distributions. These measures are the Cramer–von Mises statistic, the Anderson–Darling statistic and a measure of the distance between the quantiles of empirical and fitting distributions. We call the last method the quantile distance estimation method. Our simulation exercise shows that the quantile distance estimation method is superior to the other three methods, especially when loss data sets are relatively small and/or the fitting model is misspecified.