Daouia, Abdelaati, Padoan, Simone A. and Stupfler, Gilles Claude (2023) Extreme expectile estimation for short-tailed data, with an application to market risk assessment. TSE Working Paper, n. 23-1414, Toulouse

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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.

Item Type: Monograph (Working Paper)
Language: English
Date: March 2023
Place of Publication: Toulouse
Uncontrolled Keywords: Expectiles, Extreme values, Second-order condition, Weak dependence
Divisions: TSE-R (Toulouse)
Institution: Université Toulouse 1 Capitole
Site: UT1
Date Deposited: 08 Mar 2023 07:44
Last Modified: 17 May 2024 07:49
OAI Identifier: oai:tse-fr.eu:127937
URI: https://publications.ut-capitole.fr/id/eprint/46999
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