Affiliation:
1. School of Economics University of Sydney Sydney Australia
Abstract
AbstractThis article clarifies the relationship between pricing kernel monotonicity and the existence of opportunities for stochastic arbitrage in a complete and frictionless market of derivative securities written on a market portfolio. The relationship depends on whether the payoff distribution of the market portfolio satisfies a technical condition called adequacy, meaning that it is atomless or is comprised of finitely many equally probable atoms. Under adequacy, pricing kernel nonmonotonicity is equivalent to the existence of a strong form of stochastic arbitrage involving distributional replication of the market portfolio at a lower price. If the adequacy condition is dropped then this equivalence no longer holds, but pricing kernel nonmonotonicity remains equivalent to the existence of a weaker form of stochastic arbitrage involving second‐order stochastic dominance of the market portfolio at a lower price. A generalization of the optimal measure preserving derivative is obtained, which achieves distributional replication at the minimum cost of all second‐order stochastically dominant securities under adequacy.
Subject
Applied Mathematics,Economics and Econometrics,Social Sciences (miscellaneous),Finance,Accounting