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The Dynamics of the S&P 500 Implied Volatility Surface

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Abstract

This empirical study is motivated by the literature on “smile-consistent” arbitrage pricing with stochastic volatility. We investigate the number and shape of shocks that move implied volatility smiles and surfaces by applying Principal Components Analysis. Two components are identified under a variety of criteria. Subsequently, we develop a “Procrustes” type rotation in order to interpret the retained components. The results have implications for both option pricing and hedging and for the economics of option pricing.

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References

  • Anderson, A., A. Basilevsky, and A. Hum. (1983). “Missing Data: A Review of the Literature.” In Rossi, P., J. Wright, and A. Anderson, Handbook of Survey Research, Academic Press.

  • Barone-Adesi, G., and R. E. Whaley. (1987). “Efficient Analytic Approximation of American Option Values,” Journal of Finance 42, 301-320.

    Article  Google Scholar 

  • Basilevsky, A. (1994). Statistical Factor Analysis and Related Methods, Theory and Applications. Wiley Series in Probability and Mathematical Statistics.

  • Bates, D. S. (1988). “Pricing Options under Jump-Diffusion Processes,”Working Paper, Rodney L. White Center for Financial Research.

  • Bates, D. S. (1996). “Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options,” Review of Financial Studies 9, 69-107.

    Article  Google Scholar 

  • Black, F., and M. Scholes. (1973). “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81, 637-654.

    Article  Google Scholar 

  • Brenner, M., and D. Galai. (1987). “On the Prediction of the Implied Standard Deviation,” Advances in Futures and Options Research 2, 167-177.

    Google Scholar 

  • Buraschi, A., and J. C. Jackwerth. (1998). “Explaining Option Prices: Deterministic vs. Stochastic Models,” Working Paper, London Business School.

  • Christie, A. A. (1982). “The Stochastic Behavior of Common Stock Variances, Value, Leverage and Interest Rate Effects,” Journal of Financial Economics 10, 407-432.

    Article  Google Scholar 

  • Das, S., and R. Sundaram. (1998). “Of Smiles and Smirks: A Term-Structure Perspective,” Journal of Financial and Quantitative Analysis, forthcoming.

  • Derman, E., and I. Kani. (1998). “Stochastic Implied Trees: Arbitrage Pricing with Stochastic Term and Strike Structure of Volatility,” International Journal of Theoretical and Applied Finance 1, 61-110.

    Article  Google Scholar 

  • Dumas, B., J. Fleming, and R. E. Whaley. (1998). “Implied Volatility functions: Empirical Tests,” Journal of Finance, forthcoming.

  • Dupire, B. (1992). “Arbitrage Pricing with Stochastic Volatility,” Working Paper, Societè Generale Division Options, Paris.

  • Dupire, B. (1993). “Model Art,” Risk 6, 118-124.

    Google Scholar 

  • Frachot, A., D. Jansi, and V. Lacoste. (1992). “Factor Analysis of the Term Structure: A Probabilistic Approach,” NER, Bank of France.

  • Franks, J. R., and E. S. Schwartz. (1991). “The Stochastic Behavior of Market Variance Implied in the Prices of Index Options,” The Economic Journal 101, 1460-1475.

    Article  Google Scholar 

  • Fung, K. H., and D. A. Hsieh. (1991). “Empirical Analysis of Implied Volatility: Stocks, Bonds and Currencies,” Working Paper, Fuqua School of Business, Duke University.

  • Gallant, A. R., H. Chien, and G. Tauchen. (1998). “Calibrating Volatility Diffusions and Extracting Integrated Volatility,” Working Paper, Duke University.

  • Hamilton, J. (1994). Time Series Analysis. Princeton University Press.

  • Harvey, A. (1993). Time Series Models. Second Edition, Harvester Wheatsheaf.

  • Harvey, C. R., and R. E. Whaley. (1991). “S&P 100 Index Option Volatility,” Journal of Finance 46, 1551-1561.

    Article  Google Scholar 

  • Heath, D., R. A. Jarrow, and A. Morton. (1992). “Bond Pricing and the Term Structure of Interest Rates: A New Methodology For Contingent Claims Valuation,” Econometrica 60, 77-105.

    Article  Google Scholar 

  • Heynen, R. (1994). “An Empirical Investigation of Observed Smile Patterns,” Review of Futures Markets 13, 317-354.

    Google Scholar 

  • Hsieh, D. A. (1993): “Estimating the Dynamics of Volatility,” Proceedings of the Conference on Financial Innovation: 20 Years of Black/Scholes and Merton, Fuqua School of Business, Duke University, Durham, NC.

    Google Scholar 

  • Hsieh, D. A. (1995). “Nonlinear Dynamics in Financial Markets: Evidence and Implications,” Financial Analyst Journal 51, 55-62.

    Article  Google Scholar 

  • Hull, J., and A. White. (1987). “The Pricing of Options on Assets with Stochastic Volatilities,” Journal of Finance 42, 281-300.

    Article  Google Scholar 

  • Jackson, E. (1991). A User's Guide to Principal Components. Wiley Series in Probability and Mathematical Statistics.

  • Johnson, H., and D. Shanno. (1987). “Option Pricing when the Variance is Changing,” Journal of Financial and Quantitative Analysis 22, 143-151.

    Article  Google Scholar 

  • Kamal, M., and E. Derman. (1997). “The Patterns of Change in Implied Index Volatilities,” Goldman Sachs, Quantitative Strategies Notes.

  • Ledoit, O., and P. Santa-Clara. (1998). “Relative Pricing of Options with Stochastic Volatility,” Working Paper, University of California, Los Angeles.

  • Litterman, R., and J. Scheinkman. (1988). “Common Factors Affecting Bond Returns,” Goldman Sachs, Financial Strategies Group.

  • Merton, R. C. (1976). “Option Pricing when Underlying Stock Returns are Discontinuous,” Journal of Financial Economics 3, 125-144.

    Article  Google Scholar 

  • Roll, R. (1984). “A Simple Implicit Measure of the Effective Bid-Ask Spread,” Journal of Finance 39, 1127-1139.

    Article  Google Scholar 

  • Rubinstein, M. (1985). “Non-Parametric Tests of Alternative Option Pricing Models,” Journal of Finance 40, 455-480.

    Article  Google Scholar 

  • Schmalensee, R., and R. R. Trippi. (1978). “Common Stock Volatility Expectations Implied By Option Premia,” Journal of Finance 33, 129-147.

    Article  Google Scholar 

  • Scott, L. O. (1987). “Option Pricing when the Variance Changes Randomly: Theory, Estimation and an Application,” Journal of Financial and Quantitative Analysis 22, 419-438.

    Article  Google Scholar 

  • Scott, L. O. (1997). “Pricing Stock Options in a Jump-Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods,” Mathematical Finance 7, 413-426.

    Article  Google Scholar 

  • Stein, J. (1989). “Overreactions in the Options Market,” Journal of Finance XLIV, 1011-1023.

    Article  Google Scholar 

  • Taylor, S. J., and X. Xu. (1994). “The Magnitude of Implied Volatility Smiles: Theory and Empirical Evidence for Exchange Rates,” Review of Futures Markets 13, 355-380.

    Google Scholar 

  • Velicer, W. (1976). “Determining the Number of Components from the Matrix of Partial Correlations,” Psychometrica 41, 321-327.

    Article  Google Scholar 

  • Wiggins, J. B. (1987). “Option Values under Stochastic Volatility,” Journal of Financial Economics 19, 351-372.

    Article  Google Scholar 

  • Xu, X., and S. J. Taylor. (1994). “The Term Structure of Volatility Implied by Foreign Exchange Options,” Journal of Financial and Quantitative Analysis 29, 57-74.

    Article  Google Scholar 

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Skiadopoulos, G., Hodges, S. & Clewlow, L. The Dynamics of the S&P 500 Implied Volatility Surface. Review of Derivatives Research 3, 263–282 (2000). https://doi.org/10.1023/A:1009642705121

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