A limit order book model for latency arbitrage

TL;DR

This paper models a limit order book market with two traders of different speeds, analyzing how latency arbitrage profits can be mitigated by a Tobin tax, which enhances market efficiency and fairness.

Contribution

It introduces a model of latency arbitrage in limit order books, deriving optimal strategies under distributional uncertainty and evaluating the impact of a Tobin tax.

Findings

Fast traders can obtain risk-free profits through front-running.

A Tobin tax can eliminate arbitrage profits.

Implementing a Tobin tax improves market efficiency and attracts traders.

Abstract

We consider a single security market based on a limit order book and two investors, with different speeds of trade execution. If the fast investor can front-run the slower investor, we show that this allows the fast trader to obtain risk free profits, but that these profits cannot be scaled. We derive the fast trader's optimal behaviour when she has only distributional knowledge of the slow trader's actions, with few restrictions on the possible prior distributions. We also consider the slower trader's response to the presence of a fast trader in a market, and the effects of the introduction of a `Tobin tax' on financial transactions. We show that such a tax can lead to the elimination of profits from front-running strategies. Consequently, a Tobin tax can both increase market efficiency and attract traders to a market.