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Implied Volatility Functions: Empirical Tests

  • Bernard Dumas
  • Jeff Fleming
  • Robert E. Whaley
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    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.

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    Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 5500.

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    Date of creation: Mar 1996
    Date of revision:
    Publication status: published as The Journal of Finance, Vol. L111, no.6, (December 1998), pp. 2059-2106.
    Handle: RePEc:nbr:nberwo:5500
    Note: AP
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    1. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, . "Theory of Rational Option Pricing: II (Revised: 1-96)," Rodney L. White Center for Financial Research Working Papers 11-95, Wharton School Rodney L. White Center for Financial Research.
    2. Lo, Andrew W., 1986. "Statistical tests of contingent-claims asset-pricing models : A new methodology," Journal of Financial Economics, Elsevier, vol. 17(1), pages 143-173, September.
    3. Harvey, Campbell R & Whaley, Robert E, 1991. " S&P 100 Index Option Volatility," Journal of Finance, American Finance Association, vol. 46(4), pages 1251-61, September.
    4. 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.
    5. Robert J. Shiller, 1992. "Market Volatility," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262691515, June.
    6. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    7. Yacine Ait-Sahalia & Andrew W. Lo, 1995. "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," NBER Working Papers 5351, National Bureau of Economic Research, Inc.
    8. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    9. Whaley, Robert E., 1982. "Valuation of American call options on dividend-paying stocks : Empirical tests," Journal of Financial Economics, Elsevier, vol. 10(1), pages 29-58, March.
    10. repec:fth:inseep:9329 is not listed on IDEAS
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