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Implied Volatility Functions: Empirical Tests

Author

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  • Bernard Dumas

    (HEC Paris - Recherche - Hors Laboratoire - HEC Paris - Ecole des Hautes Etudes Commerciales)

  • Jeff Fleming
  • Robert E. Whaley

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 behaviour 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 Standard and Poors index of 500 companies (S&P 500) 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 DVF option valuation model.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Bernard Dumas & Jeff Fleming & Robert E. Whaley, 1996. "Implied Volatility Functions: Empirical Tests," Working Papers hal-00606071, HAL.
    • Handle: RePEc:hal:wpaper:hal-00606071
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    References listed on IDEAS

    as
    1. 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.
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    6. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, "undated". "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.
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    8. 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.
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    10. repec:crs:wpaper:9329 is not listed on IDEAS
    11. 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 637-654, May-June.
    12. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
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    Citations

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    Cited by:

    1. Robert Tompkins, 2001. "Implied volatility surfaces: uncovering regularities for options on financial futures," The European Journal of Finance, Taylor & Francis Journals, vol. 7(3), pages 198-230.
    2. Garcia, R. & Renault, E., 1998. "Risk Aversion, Intertemporal Substitution, and Option Pricing," Cahiers de recherche 9801, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
    3. David S. Bates, 1997. "Post-'87 Crash Fears in S&P 500 Futures Options," NBER Working Papers 5894, National Bureau of Economic Research, Inc.
    4. Joshua V. Rosenberg & Robert F. Engle, 1997. "Option Hedging Using Empirical Pricing Kernels," NBER Working Papers 6222, National Bureau of Economic Research, Inc.
    5. Peter A. Abken & Saikat Nandi, 1996. "Options and volatility," Economic Review, Federal Reserve Bank of Atlanta, vol. 81(Dec), pages 21-35.
    6. Groh, Alexander P., 2004. "Risikoadjustierte Performance von Private Equity-Investitionen," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 21382, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    7. Steven Heston & Saikat Nandi, 1997. "A closed-form GARCH option pricing model," FRB Atlanta Working Paper 97-9, Federal Reserve Bank of Atlanta.
    8. 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.
    9. Rama CONT, 1998. "Beyond implied volatility: extracting information from option prices," Finance 9804002, University Library of Munich, Germany.
    10. Garry Twite, 1996. "The Pricing of SPI Futures Options with Daily Futures Style Margin Payments," Australian Journal of Management, Australian School of Business, vol. 21(2), pages 139-157, December.
    11. Chang, Carolyn W. & S.K. Chang, Jack & Lim, Kian-Guan, 1998. "Information-time option pricing: theory and empirical evidence," Journal of Financial Economics, Elsevier, vol. 48(2), pages 211-242, May.
    12. Schmitt, Christian, 1996. "Option pricing using EGARCH models," ZEW Discussion Papers 96-20, ZEW - Leibniz Centre for European Economic Research.
    13. Carol Alexandra, 2002. "Common Correlation and Calibrating the Lognormal Forward Rate Model," ICMA Centre Discussion Papers in Finance icma-dp2002-18, Henley Business School, University of Reading, revised Jan 2003.
    14. Pena, Ignacio & Rubio, Gonzalo & Serna, Gregorio, 1999. "Why do we smile? On the determinants of the implied volatility function," Journal of Banking & Finance, Elsevier, vol. 23(8), pages 1151-1179, August.
    15. Carol Alexander, 2002. "Short and Long Term Smile Effects: The Binomial Normal Mixture Diffusion Model," ICMA Centre Discussion Papers in Finance icma-dp2003-06, Henley Business School, University of Reading, revised Mar 2003.

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    More about this item

    Keywords

    Implied Volatility Functions; Empirical Tests;

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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