The Third Fundamental Theorem of Asset Pricing

Abstract

The importance of market efficiency to derivative pricing is not well understood. The purpose of this paper is to explain this connection. The connection is established using the third fundamental theorem of asset pricing. The third fundamental theorem of asset pricing characterizes the conditions under which an equivalent martingale probability measure exists in an economy. Noting that the existence of an equivalent martingale probability measure is both necessary and sufficient for the market being informationally efficient, we prove that in a complete market, the market being efficient is both necessary and sufficient for the validity of the risk neutral valuation methodology.

Keywords: no arbitrage, completeness, no dominance, economic equilibrium, market effciency, martingale measures, local martingales