Arbitrage in markets with bid-ask spreads

TL;DR

This paper introduces the concept of an equivalent bid-ask martingale measure in markets with bid-ask spreads, proving a fundamental theorem of asset pricing and applying it to a Cox-Ross-Rubinstein model variant.

Contribution

It develops a new theoretical framework for asset pricing in markets with bid-ask spreads using EBAMM and proves a fundamental theorem of asset pricing in this context.

Findings

Established the existence of EBAMM in markets with bid-ask spreads.

Proved the fundamental theorem of asset pricing using EBAMM.

Applied the theory to a Cox-Ross-Rubinstein model with spreads.

Abstract

In this paper a finite discrete time market with an arbitrary state space and bid-ask spreads is considered. The notion of an equivalent bid-ask martingale measure (EBAMM) is introduced and the fundamental theorem of asset pricing is proved using (EBAMM) as an equivalent condition for no-arbitrage. The Cox-Ross-Rubinstein model with bid-ask spreads is presented as an application of our results.