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Predictable dynamics in the S&P 500 index options implied volatility surface

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  • Silvia Goncalves
  • Massimo Guidolin

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.

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Bibliographic Info

Paper provided by Federal Reserve Bank of St. Louis in its series Working Papers with number 2005-010.

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Date of creation: 2005
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Publication status: Published in Journal of Business, May 2006, 79(3), pp. 1591-1635
Handle: RePEc:fip:fedlwp:2005-010

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Keywords: Assets (Accounting) ; Prices;

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  1. Allan Timmermann & Massimo Guidolin, 2001. "Option Prices under Bayesian Learning: Implied Volatility Dynamics and Predictive Densities," FMG Discussion Papers dp397, Financial Markets Group.
  2. Christensen, B. J. & Prabhala, N. R., 1998. "The relation between implied and realized volatility," Journal of Financial Economics, Elsevier, vol. 50(2), pages 125-150, November.
  3. Garcia, R. & Luger, R. & Renault, E., 2001. "Empirical Assessment of an Intertemporal option Pricing Model with Latent variables," Cahiers de recherche 2001-10, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  4. Francis X. Diebold & Canlin Li, 2003. "Forecasting the Term Structure of Government Bond Yields," NBER Working Papers 10048, National Bureau of Economic Research, Inc.
  5. Christoffersen, Peter & Jacobs, Kris, 2004. "The importance of the loss function in option valuation," Journal of Financial Economics, Elsevier, vol. 72(2), pages 291-318, May.
  6. Robert F. Engle & Victor K. Ng, 1991. "Measuring and Testing the Impact of News on Volatility," NBER Working Papers 3681, National Bureau of Economic Research, Inc.
  7. Diebold, Francis X & Mariano, Roberto S, 1995. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 253-63, July.
  8. René Garcia & Eric Ghysels & Éric Renault, 2004. "The Econometrics of Option Pricing," CIRANO Working Papers 2004s-04, CIRANO.
  9. Canina, Linda & Figlewski, Stephen, 1993. "The Informational Content of Implied Volatility," Review of Financial Studies, Society for Financial Studies, vol. 6(3), pages 659-81.
  10. Day, Theodore E. & Lewis, Craig M., 1988. "The behavior of the volatility implicit in the prices of stock index options," Journal of Financial Economics, Elsevier, vol. 22(1), pages 103-122, October.
  11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  12. Bakshi, Gurdip S. & Zhiwu, Chen, 1997. "An alternative valuation model for contingent claims," Journal of Financial Economics, Elsevier, vol. 44(1), pages 123-165, April.
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Cited by:
  1. Le, Van & Zurbruegg, Ralf, 2010. "The role of trading volume in volatility forecasting," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 20(5), pages 533-555, December.
  2. Bedendo, Mascia & Hodges, Stewart D., 2009. "The dynamics of the volatility skew: A Kalman filter approach," Journal of Banking & Finance, Elsevier, vol. 33(6), pages 1156-1165, June.
  3. Konstantinidi, Eirini & Skiadopoulos, George & Tzagkaraki, Emilia, 2008. "Can the evolution of implied volatility be forecasted? Evidence from European and US implied volatility indices," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2401-2411, November.
  4. Alejandro Bernales & Massimo Guidolin, 2012. "Can We Forecast the Implied Volatility Surface Dynamics of Equity Options? Predictability and Economic Value Tests," Working Papers 456, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  5. Chalamandaris, Georgios & Tsekrekos, Andrianos E., 2011. "How important is the term structure in implied volatility surface modeling? Evidence from foreign exchange options," Journal of International Money and Finance, Elsevier, vol. 30(4), pages 623-640, June.
  6. Goulas, Lambros & Skiadopoulos, George, 2012. "Are freight futures markets efficient? Evidence from IMAREX," International Journal of Forecasting, Elsevier, vol. 28(3), pages 644-659.
  7. Dunis, Christian & Kellard, Neil M. & Snaith, Stuart, 2013. "Forecasting EUR–USD implied volatility: The case of intraday data," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 4943-4957.
  8. Chalamandaris, Georgios & Rompolis, Leonidas S., 2012. "Exploring the role of the realized return distribution in the formation of the implied volatility smile," Journal of Banking & Finance, Elsevier, vol. 36(4), pages 1028-1044.
  9. Georgios Chalamandaris & Andrianos Tsekrekos, 2013. "Explanatory Factors and Causality in the Dynamics of Volatility Surfaces Implied from OTC Asian–Pacific Currency Options," Computational Economics, Society for Computational Economics, vol. 41(3), pages 327-358, March.
  10. Chalamandaris, Georgios & Tsekrekos, Andrianos E., 2010. "Predictable dynamics in implied volatility surfaces from OTC currency options," Journal of Banking & Finance, Elsevier, vol. 34(6), pages 1175-1188, June.

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