Option Prices with Uncertain Fundamentals. Theory and Evidence on the Dynamics of211 Implied Volatilities

摘要

In an incomplete information model, investors' uncertainty about the underlying211u001edrift rate of a firm's fundamentals affects option prices through (1) endogenous 211u001eand belief-dependent stochastic volatility, (2) stochastic covariance between 211u001ereturns and volatility, and (3) a market price of 'belief risk.' For the special 211u001ecase where the drift takes only two values, we provide an option pricing formula 211u001eusing Fourier Transforms. The model calibrated to 1960-1998 S&P 500 real earnings 211u001egrowth shows that investors' uncertainty explains intertemporal variation in the 211u001eslope and curvature of implied volatility curves as well as the conditional 211u001emoments of the state-return density obtained from option data. The calibrated 211u001emodel generates hedging 'violations' of one-factor markov and deterministic 211u001evolatility function models with roughly empirical frequencies.