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The use of expectiles in risk management has recently gathered remarkablemomentum due to their excellent axiomatic and probabilistic properties. Inparticular, the class of elicitable law-invariant coherent risk measures onlyconsists of expectiles. While the theory of expectile estimation at centrallevels is substantial, tail estimation at extreme levels has so far only beenconsidered when the tail of the underlying distribution is heavy. This articleis 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 thecorresponding extreme value index is negative. We derive an asymptoticexpansion of tail expectiles in this challenging context under a generalsecond-order extreme value condition, which allows to come up with twosemiparametric estimators of extreme expectiles, and with their asymptoticproperties in a general model of strictly stationary but weakly dependentobservations. A simulation study and a real data analysis from a forecastingperspective are performed to verify and compare the proposed competingestimation procedures.

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