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 data-set of closing daily prices of FTSE MIB index options. We introduce the interexpectile difference Delta tau (X) := e(tau) (X) - e(1-tau) (X), for tau is an element of (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
Bellini, F., Mercuri, L., Rroji, E. (2018). Implicit expectiles and measures of implied volatility. QUANTITATIVE FINANCE, 18(11), 1851-1864 [10.1080/14697688.2018.1447680].
Implicit expectiles and measures of implied volatility
Bellini, Fabio;Mercuri, Lorenzo;Rroji, Edit
2018
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 data-set of closing daily prices of FTSE MIB index options. We introduce the interexpectile difference Delta tau (X) := e(tau) (X) - e(1-tau) (X), for tau is an element of (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
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