The Maximum Entropy Distribution of an Asset Inferred from Option Prices

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Abstract
This paper describes the application of the Principle of Maximum Entropy to the estimation of the distribution of an underlying asset from a set of option prices. The resulting distribution is least committal with respect to unknown or missing information and is, hence, the least prejudiced. The maximum entropy distribution is the only information about the asset that can be inferred from the price data alone. An extension to the Principle of Minimum Cross-Entropy allows the inclusion of prior knowledge of the asset distribution. We show that the maximum entropy distribution is able to accurately fit a known density, given simulated option prices at different strikes.

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