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Finance and Economics Discussion Series
The Finance and Economics Discussion Series logo links to FEDS home page Option Prices with Uncertain Fundamentals Theory and Evidence on the Dynamics of Implied Volatilities
Alexander David and 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.

Keywords: Uncertainty, changing return-volatility correlation, belief risk, put-call ratio, butterfly spread, hedging violations

Full paper (670 KB PDF) | Full paper (849 KB Postscript)

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Last update: October 20, 1999