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Option prices with uncertain fundamentals theory and evidence on the dynamics of implied volatilities

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  • Alexander David
  • Pietro Varonesi
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    Abstract

    In an incomplete information model, investors' uncertainty about the underlying drift rate of a firm's fundamentals affects option prices through (i) endogenous and belief-dependent stochastic volatility, (ii) stochastic covariance between returns and volatility, and (iii) a market price of "belief risk." For the special case where the drift takes only two values, we provide an option pricing formula using Fourier Transforms. The model calibrated to 1960-1998 S&P 500 real earnings growth shows that investors' uncertainty explains intertemporal variation in the slope and curvature of implied volatility curves as well as the conditional moments of the state-return density obtained from option data. The calibrated model generates hedging `violations' of one-factor markov and deterministic volatility function models with roughly empirical frequencies.

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    Bibliographic Info

    Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 1999-47.

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    Date of creation: 1999
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    Handle: RePEc:fip:fedgfe:1999-47

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    Keywords: Options (Finance) ; Stock - Prices;

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    References

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    1. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    2. Detemple, Jerome B, 1986. " Asset Pricing in a Production Economy with Incomplete Information," Journal of Finance, American Finance Association, vol. 41(2), pages 383-91, June.
    3. Whitney K. Newey & Kenneth D. West, 1986. "A Simple, Positive Semi-Definite, Heteroskedasticity and AutocorrelationConsistent Covariance Matrix," NBER Technical Working Papers 0055, National Bureau of Economic Research, Inc.
    4. Yaacov Z. Bergman & Bruce D. Grundy & Zvi Wiener, . "General Properties of Option Prices (Revision of 11-95) (Reprint 058)," Rodney L. White Center for Financial Research Working Papers 01-96, Wharton School Rodney L. White Center for Financial Research.
    5. Jones, Robert A & Ostroy, Joseph M, 1984. "Flexibility and Uncertainty," Review of Economic Studies, Wiley Blackwell, vol. 51(1), pages 13-32, January.
    6. Gennotte, Gerard, 1986. " Optimal Portfolio Choice under Incomplete Information," Journal of Finance, American Finance Association, vol. 41(3), pages 733-46, July.
    7. Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.
    8. Bergman, Yaacov Z & Grundy, Bruce D & Wiener, Zvi, 1996. " General Properties of Option Prices," Journal of Finance, American Finance Association, vol. 51(5), pages 1573-1610, December.
    9. Lucas, Robert E, Jr, 1978. "Asset Prices in an Exchange Economy," Econometrica, Econometric Society, vol. 46(6), pages 1429-45, November.
    10. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    11. Stein, Elias M & Stein, Jeremy C, 1991. "Stock Price Distributions with Stochastic Volatility: An Analytic Approach," Review of Financial Studies, Society for Financial Studies, vol. 4(4), pages 727-52.
    12. Yacine Ait-Sahalia, 1998. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approach," NBER Technical Working Papers 0222, National Bureau of Economic Research, Inc.
    13. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
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    Cited by:
    1. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Centre de Recherche en Economie et Statistique.
    2. Tianyu Mo & Zhenlong Zheng & William T. Lin, 2012. "The shape of option implied volatility: a study based on market net demand pressure," China Finance Review International, Emerald Group Publishing, vol. 2(1), pages 27-52, February.
    3. Ziegler, Alexandre, 2002. "State-price densities under heterogeneous beliefs, the smile effect, and implied risk aversion," European Economic Review, Elsevier, vol. 46(8), pages 1539-1557, September.
    4. Locarno, Alberto & Massa, Massimo, 2005. "Monetary Policy Uncertainty and the Stock Market," CEPR Discussion Papers 4828, C.E.P.R. Discussion Papers.

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