Pricing Stock and Bond Options in Incomplete Markets

Abstract

Modern options theory assumes that securities markets are complete and processes are known. But how should options be priced when markets are not complete and price processes are not known? The maximum-entropy framework, which formalizes the efficient market hypothesis, offers process-free option valuation in incomplete markets. This article reviews the gamma model for pricing stock options and the beta model for pricing bond options, both obtained in the maximum-entropy framework. Both models are as convenient as the Black–Scholes model, but unlike the Black–Scholes model they are valid in incomplete markets and do not restrict prices, interest rates, or volatilities to any specific paths. The gamma and beta models are both less restrictive and more accurate than alternative option valuation models.

TOPICS: Portfolio theory, factor-based models, statistical methods