No arbitrage and lead-lag relationships

TL;DR

This paper examines lead-lag relationships in financial markets, showing that models incorporating these relationships can be arbitrage-free when accounting for market frictions like transaction costs and minimal waiting times.

Contribution

It demonstrates how market frictions eliminate arbitrage opportunities in continuous-time models with lead-lag effects.

Findings

Lead-lag models can admit arbitrage without market frictions.

Market frictions such as transaction costs remove arbitrage opportunities.

Lead-lag relationships are consistent with no arbitrage when considering realistic market constraints.

Abstract

The existence of time-lagged cross-correlations between the returns of a pair of assets, which is known as the lead-lag relationship, is a well-known stylized fact in financial econometrics. Recently some continuous-time models have been proposed to take account of the lead-lag relationship. Such a model does not follow a semimartingale as long as the lead-lag relationship is present, so it admits an arbitrage without market frictions. In this paper we show that they are free of arbitrage if we take account of market frictions such as the presence of minimal waiting time on subsequent transactions or transaction costs.