Risk Management with Expectiles

22 Pages Posted: 5 Aug 2014 Last revised: 21 Dec 2014

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Elena Di Bernardino

Conservatoire National des Arts et Métiers (CNAM)

Date Written: December 21, 2014

Abstract

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

Bellini, Fabio and Di Bernardino, Elena, Risk Management with Expectiles (December 21, 2014). Available at SSRN: https://ssrn.com/abstract=2475106 or http://dx.doi.org/10.2139/ssrn.2475106

Fabio Bellini (Contact Author)

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi ( email )

Milano, Milan
Italy

Elena Di Bernardino

Conservatoire National des Arts et Métiers (CNAM) ( email )

292, rue Saint-Martin
Paris cedex 03, 75141
France

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