Keywords: Uncertainty, changing return-volatility correlation, belief risk, put-call ratio, butterfly spread, hedging violations
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 (670 KB PDF)
| Full paper (849 KB Postscript)
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Last update: October 20, 1999