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Approximating expected shortfall for heavy-tailed distributions


Broda, Simon; Krause, Jochen; Paolella, Marc (2018). Approximating expected shortfall for heavy-tailed distributions. Econometrics and Statistics, 8:184-203.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Language:English
Date:October 2018
Deposited On:07 Mar 2019 09:22
Last Modified:07 Mar 2019 09:22
Publisher:Elsevier
ISSN:2468-0389
OA Status:Closed
Publisher DOI:https://doi.org/10.1016/j.ecosta.2017.07.003
Other Identification Number:merlin-id:17162

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