Mathematics and Financial Economics

, Volume 6, Issue 3, pp 211–227 | Cite as

A limit order book model for latency arbitrage

Article

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 

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References

  1. 1.
    Alfonsi, A., Schied, A.: Optimal trade execution and absence of price manipulations in limit order book models. Working papers (2009)Google Scholar
  2. 2.
    Arnuk, S., Saluzzi, J.: Latency arbitrage: the real power behind predatory high frequency trading. Working paper (2009)Google Scholar
  3. 3.
    Bertsimas D., Lo A.: Optimal control of execution costs. J. Financ. Mark. 1(1), 1–50 (1998)CrossRefGoogle Scholar
  4. 4.
    Blais M., Protter P.: An analysis of the supply curve for liquidity risk through book data. Int. J. Theor. Appl. Financ. 13(6), 821–838 (2010)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Brunnermeier M.K., Pedersen L.H.: Predatory trading. J. Financ. 60(4), 1825–1863 (2005)CrossRefGoogle Scholar
  6. 6.
    Cvitanic, J., Kirilenko, A.A.: High frequency traders and asset prices. Cal. Tech. Working Paper (2010)Google Scholar
  7. 7.
    Delbaen F., Schachermayer W.: The mathematics of arbitrage, vol. 13. Springer, Berlin (2006)Google Scholar
  8. 8.
    Ehrenstein G., Westerhoff F., Stauffer D.: Tobin tax and market depth. Quant. Financ. 5(2), 213–218 (2005)MATHCrossRefGoogle Scholar
  9. 9.
    European Commission. Financial transaction tax: Making the financial sector pay its fair share. Press release (Ref IP/11/1085), 28 September (2011)Google Scholar
  10. 10.
    Gatheral J., Schied A., Slynko A.: Transient linear price impact and fredholm integral equations. Math. Financ. 22(3), 445–474 (2012)CrossRefGoogle Scholar
  11. 11.
    Gatheral, J., Schied, A., Slynko A.: Exponential resilience and decay of market impact. In: Econophysics of order-driven markets, pp. 225–236. Springer, Milan (2011)Google Scholar
  12. 12.
    Gökay, S., Roch, A.F., Soner, H.M.: Liquidity models in continuous and discrete time. In: Di Nunno, G. et al. (eds.) Advanced mathematical methods for finance, pp. 333–365. Springer, Berlin (2011)Google Scholar
  13. 13.
    Gould, M.D., Porter, M.A., Williams, S., McDonald, M., Fenn, D.J., Howison, S.D.: The limit order book: a survey. Arxiv preprint arXiv:1012.0349 (2010)Google Scholar
  14. 14.
    Huberman G., Stanzl W.: Price manipulation and quasi-arbitrage. Econometrica 72(4), 1247–1275 (2004)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Jarrow, R., Protter, P., Roch, A.: A liquidity based model for asset price bubbles. Quant. Financ. (forthcoming)Google Scholar
  16. 16.
    Jarrow, R.A., Protter, P.: A dysfunctional role of high frequency trading in electronic markets. Johnson School Research Paper (2011)Google Scholar
  17. 17.
    Karatzas I., Kardaras C.: The numéraire portfolio in semimartingale financial models. Financ. Stoch. 11(4), 447–493 (2007)MathSciNetMATHCrossRefGoogle Scholar
  18. 18.
    Kirilenko, A., Kyle, A., Samadi, M., Tuzun, T.: The flash crash: the impact of high frequency trading on an electronic market. Working Paper 2011, University of Maryland (2010)Google Scholar
  19. 19.
    Moallemi, C.C., Park, B., Van Roy, B.: Strategic execution in the presence of an uninformed arbitrageur. Arxiv preprint arXiv:0801.3001 (2008)Google Scholar
  20. 20.
    Palley T.I.: Speculation and tobin taxes: why sand in the wheels can increase economic efficiency. J. Econ. 69(2), 113–126 (1999)MATHCrossRefGoogle Scholar
  21. 21.
    Roch, A., Soner, H.M.: Resilient price impact of trading (2011)Google Scholar
  22. 22.
    Roch A.F.: Liquidity risk, price impacts and the replication problem. Financ. Stoch. 15(3), 399–419 (2011)Google Scholar
  23. 23.
    Schied, A., Slynko, A.: Some mathematical aspects of market impact modeling. In: Blath, J., Imkeller, P., Roelly, S. (eds.) Surveys in stochastic processes. Proceedings of the 33rd SPA, pp. 153–180. Berlin (2011)Google Scholar
  24. 24.
    Westerhoff F.: Heterogeneous traders and the tobin tax. J. Evolut. Econ. 13(1), 53–70 (2003)CrossRefGoogle Scholar
  25. 25.
    Wrobel, M.: Financial transactions taxes: the international experience and the lessons for Canada. Research Branch, Library of Parliament, Ottawa (1996)Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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