Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface

Posted: 21 Jan 2005

See all articles by Sílvia Gonçalves

Sílvia Gonçalves

University of Montreal - Department of Economics

Massimo Guidolin

Bocconi University - Department of Finance

Multiple version iconThere are 2 versions of this paper


One key stylized fact in the empirical option pricing literature is the existence of an implied volatility surface (IVS). The usual approach consists of fitting a linear model linking the implied volatility to the time to maturity and the moneyness, for each cross section of options data. However, recent empirical evidence suggests that the parameters characterizing the IVS change over time. In this paper, we study whether the resulting predictability patterns in the IVS coefficients may be exploited in practice. We propose a two-stage approach to modeling and forecasting the S&P 500 index options IVS. In the first stage, we model the surface along the cross-sectional moneyness and time-to-maturity dimensions, similarly to Dumas, et. al., (1998). In the second-stage, we model the dynamics of the cross-sectional first-stage implied volatility surface coefficients by means of vector autoregression models. We find that not only the S&P 500 implied volatility surface can be successfully modeled, but also that its movements over time are highly predictable in a statistical sense. We then examine the economic significance of this statistical predictability with mixed findings. Whereas profitable delta-hedged positions can be set up that exploit the dynamics captured by the model under moderate transaction costs and when trading rules are selective in terms of expected gains from the trades, most of this profitability disappears when we increase the level of transaction costs and trade multiple contracts off wide segments of the IVS. This suggests that predictability of the time-varying S&P 500 implied volatility surface may be not inconsistent with market efficiency.

Keywords: Implied volatility surface, predictability, trading rules

JEL Classification: G12, G13

Suggested Citation

Goncalves, Silvia and Guidolin, Massimo, Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface. Journal of Business, Vol. 79, No. 3, pp. 1591-1635, May 2006. Available at SSRN:

Silvia Goncalves

University of Montreal - Department of Economics ( email )

C.P. 6128, succursale Centre-Ville
Montreal, Quebec H3C 3J7

Massimo Guidolin (Contact Author)

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136

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