Information in Risk Neutral Probabilities

Abstract

Implicit in the prices of financial options are Arrow-Debreu prices and their continuous equivalent, the risk-neutral probability density function. Intuitively, this probability measure represents the market’s expectation of the future price of an underlying security. In this paper, we examine the evolution of the density function as an option approaches maturity. Information theory is used to quantify the information gained as the distribution becomes more and more concentrated. We propose an estimator of the density which does not bias our measurement as an alternative to other nonparametric approaches. We then estimate the density for options with the same expiration date and compute measures of information. Our parametric analysis shows the majority of information in our approximate risk-neutral measure accrues near maturity according to a logarithmic or power law. No existing theoretical model describes this process.

JEL Classifations: C14, G13, G14.

Keywords: Options pricing, implied probability density function, information & entropy