A Simple Nonparametric Approach to Derivative Security Valuation

Canonical valuation uses historical time series to predict the probability distribution of the discounted value of primary assets' discounted prices plus accumulated dividends at any future date. Then the axiomatically‐rationalized maximum entropy principle is used to estimate risk‐neutral (equivalent martingale) probabilities that correctly price the primary assets, as well as any predesignated subset of derivative securities whose payoffs occur at this date. Valuation of other derivative securities proceeds by calculation of its discounted, risk‐neutral expected value. Both simulation and empirical evidence suggest that canonical valuation has merit.