Implied Volatility Functions: Empirical Tests

36 Pages Posted: 1 Jul 1998 Last revised: 28 Nov 2012

See all articles by Bernard Dumas

Bernard Dumas

INSEAD; National Bureau of Economic Research (NBER); Centre for Economic Policy Research (CEPR)

Jeff Fleming

Rice University - Jesse H. Jones Graduate School of Business

Robert E. Whaley

Vanderbilt University - Finance

Date Written: March 1996

Abstract

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 and develop the deterministic volatility function (DVF) option valuation model, which 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 through December 1993, we evaluate the economic significance of the implied deterministic volatility function by examining the predictive and hedging performance of the DV option valuation model. We find that its performance is worse than that of an ad hoc Black-Scholes model with variable implied volatilities.

Suggested Citation

Dumas, Bernard and Fleming, Jeff and Whaley, Robert E., Implied Volatility Functions: Empirical Tests (March 1996). NBER Working Paper No. w5500. Available at SSRN: https://ssrn.com/abstract=7373

Bernard Dumas

INSEAD ( email )

Boulevard de Constance
F-77305 Fontainebleau Cedex
France
+33 1 60 72 49 92 (Phone)
+33 1 60 72 40 45 (Fax)

HOME PAGE: http://www.insead.fr/~dumas/

National Bureau of Economic Research (NBER)

1050 Massachusetts Avenue
Cambridge, MA 02138
United States

Centre for Economic Policy Research (CEPR)

London
United Kingdom

Jeff Fleming (Contact Author)

Rice University - Jesse H. Jones Graduate School of Business ( email )

6100 South Main Street
P.O. Box 1892
Houston, TX 77005-1892
United States
713-348-4677 (Phone)
713-348-5251 (Fax)

HOME PAGE: http://www.ruf.rice.edu/~jfleming

Robert E. Whaley

Vanderbilt University - Finance ( email )

401 21st Avenue South
Nashville, TN 37203
United States
615-343-7747 (Phone)
615-376-8879 (Fax)

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