Pricing of non-redundant derivatives in a complete market

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 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-Neumann Morgenstern functions. We provide numerical examples that show the applicability of the restriction for the computation of option prices.We are indebted to the editor Marti Subrahmanyam and two anonymous referees for very constructive comments. We have also benefitted from conversations with Nour Meddahi. We would like to thank seminar participants at Université de Montréal, Washington University, HEC Montréal, Ecole Polytechnique de Tunisie, Institut Henri Poincaré, Trento Mathematical Finance Conference (1997), Aspet (FIQUAM) Conference (1998) as well as the participants at the Quantitative Methods of Finance Conference, Australia, 1997.This author gratefully acknowledges the financial support of INQUIRE-Europe.