Article

Mathematics and Financial Economics

, Volume 6, Issue 3, pp 211-227

First online:

A limit order book model for latency arbitrage

  • Samuel N. CohenAffiliated withMathematical Institute, University of Oxford Email author 
  • , Lukasz SzpruchAffiliated withMathematical Institute, University of Oxford

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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 preempt 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 preemptive strategies. Consequently, a Tobin tax can both increase market efficiency and attract traders to a market.

Keywords

Limit order book Latency arbitrage High-frequency trading Tobin tax

JEL Classification

D53 G28 D43 H21 C02