Estimation Risk and Adaptive Behavior in the Pricing of Options.

We consider the effects of uncertainty in the statistical parameters of the Gaussian process in the context of the Black-Scholes option pricing model. With continuous time observation of returns, uncertainty about the variance disappears over any finite time interval, but uncertainty about the mean diminishes at the rate of 1/" tau", where "tau" is the length of the time interval of observation. In a market in which participants base their portfolio decisions on the predictive distribution of returns, option prices will be higher than in a market in which uncertainty in the mean is ignored. Even though the mean parameter, "mu," is itself irrelevant in the Black-Scholes model, uncertainty about "mu" affects option values under our behavioral assumptions. Copyright 1991 by MIT Press.