On Maximum Likelihood Estimation of Operational Loss Distributions

University of Trento Department of Economics Working Paper No. 2005-03

23 Pages Posted: 23 Mar 2005

See all articles by Marco Bee

Marco Bee

University of Trento - Department of Economics and Management

Date Written: March 3, 2005

Abstract

This paper develops a likelihood-based methodology to estimate loss distributions and compute Capital at Risk in risk management applications. In particular, we deal with the problem of estimating severity distributions with censored and truncated operational losses, for which numerical maximization of the likelihood function by means of standard optimization tools may be difficult. We show that, under the standard hypothesis of lognormal severity, maximum likelihood estimation can be performed by means of the EM algorithm. We derive the relevant equations of the algorithm and apply it to operational loss data. Finally, a simulation study shows that, In this setup, the EM algorithm has more desirable properties than both the BFGS algorithm and the Nelder-Mead simplex algorithm.

Keywords: Truncated distribution, Loss model, EM algorithm, Capital at Risk

JEL Classification: C13, C15, C21, C63

Suggested Citation

Bee, Marco, On Maximum Likelihood Estimation of Operational Loss Distributions (March 3, 2005). University of Trento Department of Economics Working Paper No. 2005-03, Available at SSRN: https://ssrn.com/abstract=678062 or http://dx.doi.org/10.2139/ssrn.678062

Marco Bee (Contact Author)

University of Trento - Department of Economics and Management ( email )

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I-38122 Trento
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