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ExpectHill estimation, extreme risk and heavy tails

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  • Daouia, Abdelaati
  • Girard, Stéphane
  • Stupfler, Gilles

Abstract

Risk measures of a financial position are traditionally based on quantiles. Replacing quantiles with their least squares analogues, called expectiles, has recently received increasing attention. The novel expectile-based risk measures satisfy all coherence requirements. We revisit their extreme value estimation for heavy-tailed distributions. First, we estimate the underlying tail index via weighted combinations of top order statistics and asymmetric least squares estimates. The resulting expectHill estimators are then used as the basis for estimating tail expectiles and Expected Shortfall. The asymptotic theory of the proposed estimators is provided, along with numerical simulations and applications to actuarial and financial data.

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  • Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2018. "ExpectHill estimation, extreme risk and heavy tails," TSE Working Papers 18-953, Toulouse School of Economics (TSE).
    • Handle: RePEc:tse:wpaper:32939
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    Cited by:

    1. Daouia, Abdelaati & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2023. "An expectile computation cookbook," TSE Working Papers 23-1458, Toulouse School of Economics (TSE).
    2. Haoyu Chen & Tiantian Mao & Fan Yang, 2024. "Estimation of the Adjusted Standard-deviatile for Extreme Risks," Papers 2411.07203, arXiv.org.
    3. Gao, Suhao & Yu, Zhen, 2023. "Parametric expectile regression and its application for premium calculation," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 242-256.
    4. Yundong Tu & Siwei Wang, 2023. "Variable Screening and Model Averaging for Expectile Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 574-598, June.
    5. Damiano Rossello, 2022. "Performance measurement with expectiles," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 343-374, June.
    6. Zaevski, Tsvetelin S. & Nedeltchev, Dragomir C., 2023. "From BASEL III to BASEL IV and beyond: Expected shortfall and expectile risk measures," International Review of Financial Analysis, Elsevier, vol. 87(C).

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    More about this item

    Keywords

    Asymmetric least squares; Coherent risk measures; Expected shortfall; Expectile; Extrapolation; Extremes; Heavy tails; Tail index;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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