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A limit order book model for latency arbitrage

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  • Samuel N. Cohen
  • Lukasz Szpruch
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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 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.

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    File URL: http://arxiv.org/pdf/1110.4811
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.4811.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.4811

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    12. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
    13. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    14. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    15. Robert A. Jarrow & Philip Protter, 2012. "A Dysfunctional Role Of High Frequency Trading In Electronic Markets," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(03), pages 1250022-1-1.
    16. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
    17. Alexandre F. Roch, 2008. "Liquidity Risk, Price Impacts and the Replication Problem," Papers 0812.2440, arXiv.org, revised Dec 2009.
    18. Frey, Stefan & Sandås, Patrik, 2009. "The impact of iceberg orders in limit order books," CFR Working Papers 09-06, University of Cologne, Centre for Financial Research (CFR).
    19. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor and Francis Journals, vol. 10(1), pages 1-18.
    20. Robert Engle & Robert Ferstenberg, 2006. "Execution Risk," NBER Working Papers 12165, National Bureau of Economic Research, Inc.
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