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Optimal execution strategies in limit order books with general shape functions

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  • Aur\'elien Alfonsi

    (CERMICS)

  • Antje Fruth
  • Alexander Schied
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    Abstract

    We consider optimal execution strategies for block market orders placed in a limit order book (LOB). We build on the resilience model proposed by Obizhaeva and Wang (2005) but allow for a general shape of the LOB defined via a given density function. Thus, we can allow for empirically observed LOB shapes and obtain a nonlinear price impact of market orders. We distinguish two possibilities for modeling the resilience of the LOB after a large market order: the exponential recovery of the number of limit orders, i.e., of the volume of the LOB, or the exponential recovery of the bid-ask spread. We consider both of these resilience modes and, in each case, derive explicit optimal execution strategies in discrete time. Applying our results to a block-shaped LOB, we obtain a new closed-form representation for the optimal strategy, which explicitly solves the recursive scheme given in Obizhaeva and Wang (2005). We also provide some evidence for the robustness of optimal strategies with respect to the choice of the shape function and the resilience-type.

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    File URL: http://arxiv.org/pdf/0708.1756
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 0708.1756.

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    Date of creation: Aug 2007
    Date of revision: Feb 2010
    Handle: RePEc:arx:papers:0708.1756

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    Web page: http://arxiv.org/

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    1. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Science & Finance (CFM) working paper archive 0307332, Science & Finance, Capital Fund Management.
    2. Markus K. Brunnermeier & Lasse Heje Pedersen, 2004. "Predatory Trading," NBER Working Papers 10755, National Bureau of Economic Research, Inc.
    3. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, Elsevier, vol. 1(1), pages 1-50, April.
    4. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2004. "Fluctuations and response in financial markets: the subtle nature of 'random' price changes," Quantitative Finance, Taylor & Francis Journals, Taylor & Francis Journals, vol. 4(2), pages 176-190.
    5. Bruce Ian Carlin & Miguel Sousa Lobo & S. Viswanathan, 2007. "Episodic Liquidity Crises: Cooperative and Predatory Trading," Journal of Finance, American Finance Association, American Finance Association, vol. 62(5), pages 2235-2274, October.
    6. Umut Çetin & Robert Jarrow & Philip Protter, 2004. "Liquidity risk and arbitrage pricing theory," Finance and Stochastics, Springer, vol. 8(3), pages 311-341, 08.
    7. Marc Potters & Jean-Philippe Bouchaud, 2002. "More statistical properties of order books and price impact," Science & Finance (CFM) working paper archive 0210710, Science & Finance, Capital Fund Management.
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