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Approximating expected shortfall for heavy-tailed distributions

Elsevier       Econometrics and Statistics

Econometrics and Statistics

Volume 8, October 2018, Pages 184-203

27,50 7,00


Approximating expected shortfall for heavy-tailed distributions


A saddlepoint approximation for evaluating the expected shortfall of financial returns under realistic distributional assumptions is derived. This addresses a need that has arisen after the Basel Committee’s proposed move from Value at Risk to expected shortfall as the mandated risk measure in its market risk framework. Unlike earlier results, the approximation does not require the existence of a moment generating function, and is therefore applicable to the heavy-tailed distributions prevalent in finance. A link is established between the proposed approximation and mean-expected shortfall portfolio optimization. Numerical examples include the noncentral t, generalized error, and α-stable distributions. A portfolio of DJIA stocks is considered in an empirical application.


CDO pricing
Mixture distributions
Portfolio optimization
Saddlepoint approximation
Stop-loss premium