A Subjective and Probabilistic Approach to Derivatives

We propose a probabilistic framework for pricing derivatives, which acknowledges that information and beliefs are subjective. Market prices can be translated into implied probabilities. In particular, futures imply returns for these implied probability distributions. We argue that volatility is not risk, but uncertainty. Non-normal distributions combine the risk in the left tail with the opportunities in the right tail -- unifying the "risk premium" with the possible loss. Risk and reward must b...