Implied volatility functions: empirical tests

Black and Scholes (1973) implied volatilities tend to be systematically related to the option’s exercise price and time to expiration. Derman and Kani (1994), Dupire (1994), and Rubinstein (1994) attribute this behavior to the fact that the Black/Scholes constant volatility assumption is violated in practice. These authors hypothesize that the volatility of the underlying asset’s return is a deterministic function of the asset price and time. Since the volatility function in their model has an arbitrary specification, the deterministic volatility (DV) option valuation model has the potential of fitting the observed cross-section of option prices exactly. Using a sample of S&P 500 index options during the period June 1988 and December 1993, we attempt to evaluate the economic significance of the implied volatility function by examining the predictive and hedging performance of the DV option valuation model. Discussion draft: September 8, 1995 _____________________________________________________________________________________ *Professor of Finance, HEC School of Management and Research Professor of Finance, Fuqua School of Business, Duke University, **Assistant Professor of Administrative Science, Jones Graduate School of Administration, Rice University and ***T. Austin Finch Foundation Professor of Business Administration, Fuqua School of Business, Duke University. This research was supported by the Futures and Options Research Center at the Fuqua School of Business, Duke University. We gratefully acknowledge discussions with Jens Jackwerth and Mark Rubinstein and comments and suggestions by Peter Boessarts, Peter Carr, Jin-Chuan Duan, Denis Talay, and the participants at the Isaac Newton Institute, Cambridge University, in April 1995 and at the Chicago Board of Trade’s Nineteenth Annual Spring Research Symposium, Chicago, Illinois, in May 1995.