Pricing of Non-redundant Derivatives in a Complete Market

Abstract

We consider a complete financial market with primitive assets and derivatives on these primitive assets. Nevertheless, the derivative as sets are non-redundant in the market, in the sense that the market is complete, only with their existence. In such a framework, we derive an equilibrium restriction on the admissible prices of derivative assets. The equilibrium condition imposes a well-ordering principle restricting the set of probability measures that qualify as candidate equivalent martingale measures. This restriction is preference free and applies whenever the utility functions belong to the general class of Von-Neuman Morgenstern functions. We provide numerical examples that show the applicability of the restriction for the computation of option prices.