Optimal measure preserving derivatives revisited

Brendan Beare

Papers from arXiv.org

Abstract: This 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.

Date: 2022-01, Revised 2022-12
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Citations: View citations in EconPapers (1)

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Journal Article: Optimal measure preserving derivatives revisited (2023)
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