Probability Distributions of Assets Inferred from Option Prices via the Principle of Maximum Entropy

This article revisits the maximum entropy algorithm in the context of recovering the probability distribution of an asset from the prices of finitely many associated European call options via partially finite convex programming. We are able to provide an effective characterization of the constraint qualification under which the problem reduces to optimizing an explicit function in finitely many variables. We also prove that the value (or objective) function is lower semicontinuous on its domain. Reference is given to a website which exploits these ideas for the efficient computation of the maximum entropy solution (MES).