Option Prices with Uncertain Fundamentals: Theory and Evidence on the Dynamics of Implied Volatilities

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Abstract
In an imcomplete information model, we show that investors' uncertainty about the drift of a firm's fundamentals affects option prices through its affect on stock volatility and the covariance between returns and volatility. We provide an option pricing formula using Fourier Transforms. Filtered investor beliefs from real earnings growth are able to explain time-variation in implied volatility, the skewness premium, and the kurtosis premium embedded in option prices. Option-implied investor beliefs vacillated rapidly before the crash of 1987, remained highly uncertain for a year afterwards, and except for the 1990-91 recession, strongly favored rapid growth until 1996. Model fits to cross-sectional option prices are almost comparable to Heston's (1993) stochastic volatility model while hedging and variance forecasting performance is superior.

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