The Law of One Price in Mean–Variance Hedging

Abstract

The law of one price (LOP) broadly asserts that identical financial flows should command the same price. This paper uncovers a new mechanism through which LOP can fail in a continuous-time L2(P) setting without frictions, namely "trading from just before a predictable stopping time," which surprisingly identifies LOP violations even for continuous price processes. Closing this loophole allows to give a version of the "Fundamental Theorem of Asset Pricing'' appropriate in the quadratic context, establishing the equivalence of the economic concept of LOP with the probabilistic property of the existence of a local E-martingale state price density. The latter provides unique prices for all square-integrable contingent claims in an extended market and subsequently plays an important role in mean-variance hedging.

Keywords: Law of one price, efficient frontier, mean-variance hedging, E-density

JEL Classification: G11, G12, C61