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State Prices and Gibbs States

The foundation for the theory of asset prices in the absence of riskless arbitrage opportunities is the existence and use of normalized Arrow-Debreu state prices, also called a risk neutral probability distribution. Under this distribution, an asset's price is predicted to be the risklessly discounted, present value of its future payoff. The Bayesian, information theoretic view of inference directs us to use a generalized exponential distribution solving a constrained entropy problem (i.e. a Gibbs state), as an estimator of these risk-neutral probabilities. Use of the Gibbs state provides simple derivation of powerful asset pricing predictions, and also uncovers an isomorphism between statistical mechanics and asset pricing, paving the way for future development of new asset pricing predictions which exploit the isomorphism. The paper uses only simple mathematics to make these points, and is self-contained, in the hope that it will stimulate additional interdisciplinary interest in financial economics.