Finance and Economics Discussion Series (FEDS)
October 1999
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.
Full paper (849 KB Postscript)Keywords: Uncertainty, changing return-volatility correlation, belief risk, put-call ratio, butterfly spread, hedging violations
PDF: Full Paper
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