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Optimal order placement in limit order markets

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Author Info

  • Rama Cont

    ()
    (LPMA - Laboratoire de Probabilités et Modèles Aléatoires - CNRS : UMR7599 - Université Paris VI - Pierre et Marie Curie - Université Paris VII - Paris Diderot)

  • Arseniy Kukanov

    (Columbia University - Columbia University)

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    Abstract

    To execute a trade, participants in electronic equity markets may choose to submit limit orders or market orders across various exchanges where a stock is traded. This decision is influenced by the characteristics of the order flow and queue sizes in each limit order book, as well as the structure of transaction fees and rebates across exchanges. We propose a quantitative framework for studying this order placement problem by formulating it as a convex optimization problem. This formulation allows to study how the interplay between the state of order books, the fee structure, order flow properties and preferences of a trader determine the optimal placement decision. In the case of a single exchange, we derive an explicit solution for the optimal split between limit and market orders. For the general problem of order placement across multiple exchanges, we propose a stochastic algorithm for computing the optimal policy and study the sensitivity of the solution to various parameters using a numerical implementation of the algorithm.

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    File URL: http://hal.archives-ouvertes.fr/docs/00/73/76/13/PDF/OrderRoutingV6.pdf
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    Bibliographic Info

    Paper provided by HAL in its series Working Papers with number hal-00737491.

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    Date of creation: 01 Oct 2012
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    Handle: RePEc:hal:wpaper:hal-00737491

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00737491
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    Web page: http://hal.archives-ouvertes.fr/

    Related research

    Keywords: order routing; limit order book; limit order market; liquidity; optimal order execution; transaction costs; market microstructure;

    This paper has been announced in the following NEP Reports:

    References

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    1. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Papers 1204.0148, arXiv.org, revised Jun 2013.
    2. Thierry Foucault & Albert J. Menkveld, 2008. "Competition for Order Flow and Smart Order Routing Systems," Journal of Finance, American Finance Association, vol. 63(1), pages 119-158, 02.
    3. Fabien Guilbaud & Huyên Pham, 2012. "Optimal High Frequency Trading in a Pro-Rata Microstructure with Predictive Information," Working Papers hal-00697125, HAL.
    4. Fabien Guilbaud & Huy\^en Pham, 2012. "Optimal High Frequency Trading in a Pro-Rata Microstructure with Predictive Information," Papers 1205.3051, arXiv.org.
    5. Aur\'elien Alfonsi & Antje Fruth & Alexander Schied, 2007. "Optimal execution strategies in limit order books with general shape functions," Papers 0708.1756, arXiv.org, revised Feb 2010.
    6. Sophie Laruelle & Charles-Albert Lehalle & Gilles Pagès, 2009. "Optimal split of orders across liquidity pools: a stochastic algorithm approach," Working Papers hal-00422427, HAL.
    7. Aurelien Alfonsi & Antje Fruth & Alexander Schied, 2010. "Optimal execution strategies in limit order books with general shape functions," Quantitative Finance, Taylor & Francis Journals, vol. 10(2), pages 143-157.
    8. Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
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