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...

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Bibliographic Details
Published inThe Financial review (Buffalo, N.Y.) Vol. 26; no. 1; pp. 15 - 30
Main Authors Barry, Christopher B., French, Dan W., Rao, Ramesh K. S.
Format Journal Article
LanguageEnglish
Published Oxford, UK Blackwell Publishing Ltd 01.02.1991
Subjects
Bayesian analysis
Mathematical models
Options
Pricing
Securities prices
Stochastic models
Studies
Valuation
Variables
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Summary: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/τ, where T 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, μ, is itself irrelevant in the Black‐Scholes model, uncertainty about μ affects option values under our behavioral assumptions.
Bibliography:ArticleID:FIRE15
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ISSN:0732-8516
1540-6288
DOI:10.1111/j.1540-6288.1991.tb00367.x