Maximum Likelihood Estimation Error and Operational Value-at-Risk Stability

24 Pages Posted: 8 Apr 2019

Date Written: March 27, 2019


The challenge of using small sample sizes for operational risk capital models fitted via maximum likelihood estimation is well recognized, yet the literature generally provides warning examples rather than a systematic approach. We present a general framework for analyzing maximum likelihood estimation error on operational value-at-risk as a function of sample size for five severity distributions commonly used in operational risk capital models. More specifically, we study the estimation error along three dimensions: the choice of severity distribution, the sample size and the heaviness of the underlying losses. We apply these results to model selection and explore implications for operational risk modeling.

Keywords: heavy-tailed distributions, maximum likelihood estimation, model selection, operational risk models, small sample size, subexponential distributions

Suggested Citation

Larsen, Paul, Maximum Likelihood Estimation Error and Operational Value-at-Risk Stability (March 27, 2019). Journal of Operational Risk, Vol. 14, No. 1, 2019. Available at SSRN:

Paul Larsen (Contact Author)

Allianz SE ( email )

Königinstrasse 28
Munich, 80802

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