Estimating the lognormal-gamma model of operational risk using the Markov chain Monte Carlo method

Bakhodir Ergashev

Abstract

ABSTRACT

The lognormal-gamma distribution, being a heavy-tailed distribution, is very attractive from an operational risk modeling perspective because historical operational losses also exhibit heavy tails. Unfortunately, fitting this model requires two severe challenges to be properly addressed. First, the density function of the lognormal-gamma distribution is expressed in the form of a Lebesgue integral. Second, if the information contained in a sample of losses is insufficient to accurately estimate the shape of the distribution’s tail, the capital estimates become extremely volatile. We address both challenges by using the Markov chain Monte Carlo method and imposing prior assumptions about the model’s unknown parameters.