ExpectHill estimation, extreme risk and heavy tails

Abdelaati Daouia, Stéphane Girard and Gilles Stupfler

Journal of Econometrics, 2021, vol. 221, issue 1, 97-117

Abstract: Risk measures of a financial position are, from an empirical point of view, mainly 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.

Keywords: Asymmetric least squares; Coherent risk measures; Expected shortfall; Expectile; Extrapolation; Extremes; Heavy tails; Tail index (search for similar items in EconPapers)
JEL-codes: C13 C14 (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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Working Paper: ExpectHill estimation, extreme risk and heavy tails (2018)
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:221:y:2021:i:1:p:97-117

DOI: 10.1016/j.jeconom.2020.02.003

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