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The Equity Premium and The Volatility Spread: The Role of Risk-Neutral Skewness

54 Pages Posted: 17 Nov 2008 Last revised: 17 Dec 2016

Bruno Feunou

Bank of Canada

Jean-Sebastien Fontaine

Bank of Canada

Roméo Tédongap

ESSEC Business School

Date Written: June 1, 2009

Abstract

We introduce the Homoscedastic Gamma [HG] model where the distribution of returns is characterized by its mean, variance and an independent skewness parameter under both measures. The model predicts that the spread between historical and risk-neutral volatilities is a function of the risk premium and of skewness. In fact, the equity premium is twice the ratio of the volatility spread to skewness. We measure skewness from option prices and test these predictions. We find that conditioning on skewness increases the predictive power of the volatility spread and that coefficient estimates accord with theory. In short, the data do not reject the model’s implications for the equity premium. We also check the model’s implications for option pricing and show that the information content of skewness leads to improved in-sample and out-of-sample pricing performances as well as improved hedging performances. Our results imply that expanding around the Gaussian density is restrictive and does not offer sufficient flexibility to match the skewness and kurtosis implicit in option data. Finally, we document the term structure of option-implied volatility, skewness and kurtosis and find that time-dependence in returns has a greater impact on skewness.

Keywords: Option Prices, Skewness, Volatility Spread, Risk Premium

JEL Classification: G12, G13

Suggested Citation

Feunou, Bruno and Fontaine, Jean-Sebastien and Tédongap, Roméo, The Equity Premium and The Volatility Spread: The Role of Risk-Neutral Skewness (June 1, 2009). Review of Derivatives Research, Forthcoming; EFA 2009 Bergen Meetings Paper. Available at SSRN: https://ssrn.com/abstract=1301696 or http://dx.doi.org/10.2139/ssrn.1301696

Bruno Feunou

Bank of Canada ( email )

234 Wellington Street
Ottawa, Ontario K1A 0G9
Canada
613-782-8302 (Phone)

HOME PAGE: http://kamkui.net/

Jean-Sebastien Fontaine (Contact Author)

Bank of Canada ( email )

234 Wellington Street
Ontario, Ottawa K1A 0G9
Canada

HOME PAGE: http://www.jean-sebastienfontaine.com

Roméo Tédongap

ESSEC Business School ( email )

Avenue Bernard Hirsch
BP 105 Cergy Cedex, 95021
France
+33134439734 (Phone)
+33134439734 (Fax)

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