ExpectHill estimation, extreme risk and heavy tails

Daouia, Abdelaati, Girard, Stéphane and Stupfler, Gilles (2018) ExpectHill estimation, extreme risk and heavy tails. TSE Working Paper, n. 18-953, Toulouse

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Official URL: http://tse-fr.eu/pub/32939

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.

Item Type: Monograph (Working Paper)
Language: English
Date: September 2018
Place of Publication: Toulouse
Uncontrolled Keywords: Asymmetric least squares, Coherent risk measures, Expected shortfall, Expectile, Extrapolation, Extremes, Heavy tails, Tail index
JEL codes: C13 - Estimation
C14 - Semiparametric and Nonparametric Methods
Subjects: B- ECONOMIE ET FINANCE
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 19 Sep 2018 09:31
Last Modified: 19 Sep 2018 09:31
OAI ID: oai:tse-fr.eu:32939
URI: http://publications.ut-capitole.fr/id/eprint/26253

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