Risk Management with Expectiles
22 Pages Posted: 5 Aug 2014 Last revised: 21 Dec 2014
Date Written: December 21, 2014
Expectiles (EVaR) are a one-parameter family of coherent risk measures that have been recently suggested as an alternative to quantiles (VaR) and to Expected Shortfall (ES). In this work we review their known properties, we discuss their financial meaning, we compare them with VaR and ES and we study their asymptotic behaviour, refining some of the results in Bellini et al. (2014). Moreover, we present a numerical example of computation of expectiles by means of simple Garch(1,1) models and we assess the accuracy of the forecasts by means of a consistent loss function, as suggested by Gneiting (2011). Theoretical and numerical results indicate that expectiles are perfectly reasonable alternatives to VaR and ES.
Keywords: Expectiles, Gain-Loss, Garch, Lambert W, Extreme Value Theory
JEL Classification: G32, C14, C65
Suggested Citation: Suggested Citation