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ExpectHill estimation, extreme risk and heavy tails

Abdelaati Daouia 1 Stephane Girard 2, 3 Gilles Stupfler 4
2 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
Grenoble INP [2020-....] - Institut polytechnique de Grenoble - Grenoble Institute of Technology [2020-....], Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann
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.
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Abdelaati Daouia, Stephane Girard, Gilles Stupfler. ExpectHill estimation, extreme risk and heavy tails. Journal of Econometrics, Elsevier, In press, pp.1-54. ⟨10.1016/j.jeconom.2020.02.003⟩. ⟨hal-01856212v2⟩

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