Fat tails, expected shortfall and the Monte Carlo method: a note

Michael Brunner, Fabio Piacenza, Fabio Monti and Davide Bazzarello

Journal of Operational Risk

Abstract: ABSTRACT The expected shortfall or conditional value-at-risk is discussed as often it is now recommended as an alternative to the risk measure of value-at-risk. At the same time, the Monte Carlo method is widely used as a way to derive a statistical approximation of the results. In this note, it is demonstrated that the Monte Carlo method can have extremely bad convergence properties for heavy tailed distributions in combination with specific risk measures, including conditional value-at-risk.

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