Implicit Expectiles and Measures of Implied Volatility

19 Pages Posted: 6 Sep 2017 Last revised: 7 May 2018

See all articles by Fabio Bellini

Fabio Bellini

University of Milano Bicocca - Dipartimento di Statistica e Metodi Quantitativi

Lorenzo Mercuri

University of Milan

Edit Rroji

Polytechnic University of Milan - Department of Mathematics

Date Written: May 2018, 2017

Abstract

We show how to compute the expectiles of the risk neutral distribution from the prices of European call and put options. Empirical properties of these implicit expectiles are studied on a dataset of closing daily prices of FTSE MIB index options. We introduce the interexpectile difference Δτ (X) := eτ (X) - e1-τ (X), for τ ∈ (1/2,1], and suggest that it is a natural measure of the variability of the risk neutral distribution.

We investigate its theoretical and empirical properties and compare it with the VIX index computed by CBOE and with implicit VaR and CVaR introduced in Barone Adesi (2016).

Keywords: Implied Volatility; VIX Index; Expectiles; Interexpectile difference

JEL Classification: C00; C02; C53; G31

Suggested Citation

Bellini, Fabio and Mercuri, Lorenzo and Rroji, Edit, Implicit Expectiles and Measures of Implied Volatility (May 2018, 2017). Available at SSRN: https://ssrn.com/abstract=3031175 or http://dx.doi.org/10.2139/ssrn.3031175

Fabio Bellini

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

Milano, Milan
Italy

Lorenzo Mercuri

University of Milan ( email )

Via Festa del Perdono, 7
Milan, 20122
Italy

Edit Rroji (Contact Author)

Polytechnic University of Milan - Department of Mathematics ( email )

Via Bonardi, 9
Milano, MI 20133
Italy

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