The Dynamics of the S&P 500 Implied Volatility Surface

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.

[1]  R. Trippi,et al.  COMMON STOCK VOLATILITY EXPECTATIONS IMPLIED BY OPTION PREMIA , 1978 .

[2]  David S. Bates.  Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Thephlx Deutschemark Options , 1993 .

[3]  A. Harvey.  Time series models , 1983 .

[4]  James D. Hamilton.  Time Series Analysis , 1994 .

[5]  David Hsieh.  Nonlinear Dynamics in Financial Markets: Evidence and Implications , 1995 .

[6]  James B. Wiggins.  Option values under stochastic volatility: Theory and empirical estimates , 1987 .

[7]  D. Heath,et al.  Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation , 1990, Journal of Financial and Quantitative Analysis.

[8]  B. Dumas,et al.  Implied volatility functions: empirical tests , 1996, IEEE Conference on Computational Intelligence for Financial Engineering & Economics.

[9]  R. C. Merton,et al.  Option pricing when underlying stock returns are discontinuous , 1976 .

[10]  A. Basilevsky.  Statistical Factor Analysis and Related Methods: Theory and Applications , 1994 .

[11]  A. Christie,et al.  The stochastic behavior of common stock variances: value , 1982 .

[12]  G. Barone-Adesi,et al.  Efficient Analytic Approximation of American Option Values , 1987 .

[13]  J. E. Jackson.  A User's Guide to Principal Components , 1991 .

[14]  D. Shanno,et al.  Option Pricing when the Variance Is Changing , 1987, Journal of Financial and Quantitative Analysis.

[15]  Olivier Ledoit,et al.  Relative Pricing of Options with Stochastic Volatility , 1998 .

[16]  F. Black,et al.  The Pricing of Options and Corporate Liabilities , 1973, Journal of Political Economy.

[17]  Eduardo S. Schwartz,et al.  The Stochastic Behaviour of Market Variance Implied in the Prices of Index Options , 1991 .

[18]  Campbell R. Harvey,et al.  S&P 100 Index Option Volatility , 1991 .

[19]  Alexander Basilevsky,et al.  Chapter 12 – Missing Data: A Review of the Literature , 1983 .

[20]  R. Sundaram,et al.  Of Smiles and Smirks: A Term Structure Perspective , 1998, Journal of Financial and Quantitative Analysis.

[21]  Louis O. Scott.  Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods , 1997 .

[22]  Emanuel Derman,et al.  STOCHASTIC IMPLIED TREES: ARBITRAGE PRICING WITH STOCHASTIC TERM AND STRIKE STRUCTURE OF VOLATILITY , 1998 .

[23]  R. Roll,et al.  A Simple Implicit Measure of the Effective Bid-Ask Spread in an Efficient Market , 2008 .

[24]  W. Velicer.  Determining the number of components from the matrix of partial correlations , 1976 .

[25]  J. Rosenberg.  Implied Volatility Functions , 2000 .

[26]  Stephen L Taylor,et al.  The magnitude of implied volatility smiles: theory and empirical evidence for exchange rates , 1994 .

[27]  J. Stein.  Overreactions in the Options Market , 1989 .

[28]  Alan G. White,et al.  The Pricing of Options on Assets with Stochastic Volatilities , 1987 .

[29]  Stephen Michael Taylor,et al.  The Term Structure of Volatility Implied by Foreign Exchange Options , 1994, Journal of Financial and Quantitative Analysis.

[30]  M. Rubinstein..  Nonparametric tests of alternative option pricing models using all reported trades and quotes on the , 1985 .

[31]  Robert B. Litterman,et al.  Common Factors Affecting Bond Returns , 1991 .

[32]  Louis O. Scott.  Option Pricing when the Variance Changes Randomly: Theory, Estimation, and an Application , 1987, Journal of Financial and Quantitative Analysis.

[33]  James D. Wright,et al.  Handbook of Survey Research. , 1985 .