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Implied Volatility Functions: Empirical Tests

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

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    Bibliographic Info

    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
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    Publication status: published as The Journal of Finance, Vol. L111, no.6, (December 1998), pp. 2059-2106.
    Handle: RePEc:nbr:nberwo:5500

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    1. Whaley, Robert E., 1982. "Valuation of American call options on dividend-paying stocks : Empirical tests," Journal of Financial Economics, Elsevier, Elsevier, vol. 10(1), pages 29-58, March.
    2. Lo, Andrew W., 1986. "Statistical tests of contingent-claims asset-pricing models : A new methodology," Journal of Financial Economics, Elsevier, Elsevier, vol. 17(1), pages 143-173, September.
    3. Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, American Finance Association, vol. 49(3), pages 771-818, July.
    4. Harvey, Campbell R & Whaley, Robert E, 1991. " S&P 100 Index Option Volatility," Journal of Finance, American Finance Association, American Finance Association, vol. 46(4), pages 1251-61, September.
    5. Bossaerts, Peter & Hillion, Pierre, 1997. "Local parametric analysis of hedging in discrete time," Journal of Econometrics, Elsevier, Elsevier, vol. 81(1), pages 243-272, November.
    6. repec:fth:inseep:9329 is not listed on IDEAS
    7. 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, Wharton School Rodney L. White Center for Financial Research 11-95, Wharton School Rodney L. White Center for Financial Research.
    8. Robert J. Shiller, 1992. "Market Volatility," MIT Press Books, The MIT Press, The MIT Press, edition 1, volume 1, number 0262691515, December.
    9. Yacine Aït-Sahalia & Andrew W. Lo, . "Nonparametric Estimation of State-Price Densities Implicit in Financial Asset Prices," CRSP working papers, Center for Research in Security Prices, Graduate School of Business, University of Chicago 332, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
    10. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers, University of California at Berkeley RPF-232, University of California at Berkeley.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
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    Cited by:
    1. Pena, Ignacio & Rubio, Gonzalo & Serna, Gregorio, 1999. "Why do we smile? On the determinants of the implied volatility function," Journal of Banking & Finance, Elsevier, Elsevier, vol. 23(8), pages 1151-1179, August.
    2. Peter A. Abken & Saikat Nandi, 1996. "Options and volatility," Economic Review, Federal Reserve Bank of Atlanta, Federal Reserve Bank of Atlanta, issue Dec, pages 21-35.
    3. GARCIA, René & RENAULT, Éric, 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 9801, Universite de Montreal, Departement de sciences economiques.
    4. Zsembery, Levente, 2003. "A volatilitás előrejelzése és a visszaszámított modellek
      [Forecasting of volatility and implied models]
      ," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(6), pages 519-542.
    5. David S. Bates, 1997. "Post-'87 Crash Fears in S&P 500 Futures Options," NBER Working Papers 5894, National Bureau of Economic Research, Inc.
    6. Joshua V. Rosenberg & Robert F. Engle, 1997. "Option Hedging Using Empirical Pricing Kernels," NBER Working Papers 6222, National Bureau of Economic Research, Inc.
    7. Robert Tompkins, 2001. "Implied volatility surfaces: uncovering regularities for options on financial futures," The European Journal of Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 7(3), pages 198-230.
    8. Rama CONT, 1998. "Beyond implied volatility: extracting information from option prices," Finance, EconWPA 9804002, EconWPA.
    9. Steven L. Heston & Saikat Nandi, 1997. "A closed-form GARCH option pricing model," Working Paper, Federal Reserve Bank of Atlanta 97-9, Federal Reserve Bank of Atlanta.

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