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

42 Pages Posted: 16 Jun 2003

See all articles by Sílvia Gonçalves

Sílvia Gonçalves

University of Montreal - Department of Economics; McGill University - Department of Economics

Massimo Guidolin

affiliation not provided to SSRN; Bocconi University - Department of Finance

Multiple version iconThere are 2 versions of this paper

Date Written: November 2004

Abstract

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 strategies

JEL Classification: G12, G13

Suggested Citation

Goncalves, Silvia and Guidolin, Massimo and Guidolin, Massimo, Predictable Dynamics in the S&P 500 Index Options Implied Volatility Surface (November 2004). Available at SSRN: https://ssrn.com/abstract=406697 or http://dx.doi.org/10.2139/ssrn.406697

Silvia Goncalves

University of Montreal - Department of Economics ( email )

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

McGill University - Department of Economics ( email )

855 Sherbrooke Street West
Montreal, QC H3A 2T7
CANADA

Massimo Guidolin (Contact Author)

Bocconi University - Department of Finance ( email )

Via Roentgen 1
Milano, MI 20136
Italy

affiliation not provided to SSRN

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