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.
Expectiles; Extreme values; Second-order condition; Short tails; Weak dependence;
Abdelaati Daouia, Simone A. Padoan, and Gilles Stupfler, “Extreme expectile estimation for short-tailed data, with an application to market risk assessment”, TSE Working Paper, n. 23-1414, March 2023.
TSE Working Paper, n. 23-1414, March 2023