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 assets 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 derivatives assets. The equilibrium condition imposes a well-ordering principle equivalent martingale measures. This restriction is preference free and applies whenever the utility functions belong to the general class of Von-Neumann Morgenstern functions. We provide numerical examples that show the applicability of restriction for the computation of option prices.