Some No-Arbitrage Rules For Converging Asset Prices under Short-Sales Constraints

TL;DR

This paper investigates no-arbitrage conditions for converging asset prices under short-sale constraints, introducing structure conditions and fundamental supermartingale measures, and analyzing arbitrage portfolios when certain conditions fail.

Contribution

It translates NFLVR-S conditions into structure conditions, introduces the concept of fundamental supermartingale measure, and characterizes arbitrage portfolios in converging prices scenarios.

Findings

Established equivalence between NFLVR-S and supermartingale measures under constraints

Defined structure conditions for price processes under short-sale restrictions

Identified arbitrage portfolios when key conditions are not met

Abstract

Under short sales prohibitions, no free lunch with vanishing risk (NFLVR-S) is known to be equivalent to the existence of an equivalent supermartingale measure for the price processes (Pulido [22]). For two given price processes, we translate the property (NFLVR-S) in terms of so called structure conditions and we introduce the concept of fundamental supermartingale measure. When a certain condition necessary to the construction of the fundamental martingale measure is not fulfilled, we provide the corresponding arbitrage portfolios. The motivation of our study lies in understanding the particular case of converging prices, i.e., that are going to cross at a bounded random time.