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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 Veronesi

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.

Suggested Citation

  • Alexander David & Pietro Veronesi, 1999. "Option prices with uncertain fundamentals theory and evidence on the dynamics of implied volatilities," Finance and Economics Discussion Series 1999-47, Board of Governors of the Federal Reserve System (U.S.).
    • Handle: RePEc:fip:fedgfe:1999-47
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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, Center for Research in Economics and Statistics.
    2. Massa, Massimo & Locarno, Alberto, 2005. "Monetary Policy Uncertainty and the Stock Market," CEPR Discussion Papers 4828, C.E.P.R. Discussion Papers.
    3. Du, Ke & Fu, Yishu & Qin, Zhenjiang & Zhang, Shuoxun, 2020. "Regime shift, speculation, and stock price," Research in International Business and Finance, Elsevier, vol. 52(C).
    4. 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.
    5. 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 Limited, vol. 2(1), pages 27-52, January.

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    Keywords

    options; Stock - Prices;

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