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Approximating expected shortfall for heavy-tailed distributions

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  • Broda, Simon A.
  • Krause, Jochen
  • Paolella, Marc S.

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.

Suggested Citation

  • Broda, Simon A. & Krause, Jochen & Paolella, Marc S., 2018. "Approximating expected shortfall for heavy-tailed distributions," Econometrics and Statistics, Elsevier, vol. 8(C), pages 184-203.
    • Handle: RePEc:eee:ecosta:v:8:y:2018:i:c:p:184-203
    DOI: 10.1016/j.ecosta.2017.07.003
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    Cited by:

    1. Bruno Bouchard & Adil Reghai & Benjamin Virrion, 2020. "Computation of Expected Shortfall by fast detection of worst scenarios," Working Papers hal-02619589, HAL.
    2. Hallin, Marc & Trucíos, Carlos, 2023. "Forecasting value-at-risk and expected shortfall in large portfolios: A general dynamic factor model approach," Econometrics and Statistics, Elsevier, vol. 27(C), pages 1-15.
    3. Bruno Bouchard & Adil Reghai & Benjamin Virrion, 2020. "Computation of Expected Shortfall by fast detection of worst scenarios," Papers 2005.12593, arXiv.org.

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