Extreme expectile estimation for short-tailed data, with an application to market risk assessment

Abdelaati Daouia, Simone A. Padoan and Gilles Stupfler

No 23-1414, TSE Working Papers from Toulouse School of Economics (TSE)

Abstract: The use of expectiles in risk management has recently gathered remarkable momentum due to their excellent axiomatic and probabilistic properties. In particular, the class of elicitable law-invariant coherent risk measures only consists of expectiles. While the theory of expectile estimation at central levels is substantial, tail estima- tion at extreme levels has so far only been considered when the tail of the underlying distribution is heavy. This article is the first work to handle the short-tailed setting where the loss (e.g. negative log-returns) distribution of interest is bounded to the right and the corresponding extreme value index is negative. We derive an asymptotic expansion of tail expectiles in this challenging context under a general second-order extreme value condition, which allows to come up with two semiparametric estima- tors of extreme expectiles, and with their asymptotic properties in a general model of strictly stationary but weakly dependent observations. A simulation study and a real data analysis from a forecasting perspective are performed to verify and compare the proposed competing estimation procedures.

Keywords: Expectiles; Extreme values; Second-order condition; Weak dependence (search for similar items in EconPapers)
Date: 2023-03-07, Revised 2024-05
New Economics Papers: this item is included in nep-ecm
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