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Optimal execution strategies in limit order books with general shape functions

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Author Info

  • Aurelien Alfonsi
  • 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 modelling 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 of a risk-neutral investor, 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://www.tandfonline.com/doi/abs/10.1080/14697680802595700
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    Bibliographic Info

    Article provided by Taylor and Francis Journals in its journal Quantitative Finance.

    Volume (Year): 10 (2010)
    Issue (Month): 2 ()
    Pages: 143-157

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    Handle: RePEc:taf:quantf:v:10:y:2010:i:2:p:143-157

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    Related research

    Keywords: Liquidity risk; Optimal portfolio liquidation; Block trade execution; Limit order book; Market impact model; Market order;

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    Citations

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    Cited by:
    1. Erhan Bayraktar & Michael Ludkovski, 2011. "Liquidation in Limit Order Books with Controlled Intensity," Papers 1105.0247, arXiv.org, revised Jan 2012.
    2. Aur\'elien Alfonsi & Jos\'e Infante Acevedo, 2012. "Optimal execution and price manipulations in time-varying limit order books," Papers 1204.2736, arXiv.org.
    3. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Working Papers hal-00737491, HAL.
    4. Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Optimal Portfolio Liquidation with Limit Orders," Papers 1106.3279, arXiv.org, revised Jul 2012.
    5. Charles-Albert Lehalle, 2013. "Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process," Papers 1302.4592, arXiv.org.
    6. Peter Kratz & Torsten Sch\"oneborn, 2012. "Portfolio liquidation in dark pools in continuous time," Papers 1201.6130, arXiv.org, revised Aug 2012.
    7. Kovaleva, P. & Iori, G., 2012. "Optimal Trading Strategies in a Limit Order Market with Imperfect Liquidity," Working Papers 12/05, Department of Economics, City University London.
    8. Kervel, V.L. van, 2013. "Competition between stock exchanges and optimal trading," Open Access publications from Tilburg University urn:nbn:nl:ui:12-5663709, Tilburg University.
    9. Antje Fruth & Torsten Schoeneborn & Mikhail Urusov, 2011. "Optimal trade execution and price manipulation in order books with time-varying liquidity," Papers 1109.2631, arXiv.org.
    10. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Papers 1204.0148, arXiv.org, revised Apr 2013.
    11. Sophie Laruelle & Charles-Albert Lehalle & Gilles Pag\`es, 2011. "Optimal posting price of limit orders: learning by trading," Papers 1112.2397, arXiv.org, revised Sep 2012.
    12. Rossella Agliardi & Ramazan Gençay, 2012. "Hedging through a Limit Order Book with Varying Liquidity," Working Paper Series 12_12, The Rimini Centre for Economic Analysis.
    13. Alexandre Roch, 2011. "Liquidity risk, price impacts and the replication problem," Finance and Stochastics, Springer, vol. 15(3), pages 399-419, September.
    14. Rama Cont & Adrien De Larrard, 2013. "Price Dynamics in a Markovian Limit Order Market," Post-Print hal-00552252, HAL.
    15. Rene Carmona & Kevin Webster, 2012. "High Frequency Market Making," Papers 1210.5781, arXiv.org.
    16. Takashi Kato, 2011. "An Optimal Execution Problem in Geometric Ornstein-Uhlenbeck Price Process," Papers 1107.1787, arXiv.org, revised May 2012.
    17. Aurélien Alfonsi & Alexander Schied, 2010. "Optimal trade execution and absence of price manipulations in limit order book models," Post-Print hal-00397652, HAL.
    18. Aurélien Alfonsi & José Infante Acevedo, 2012. "Optimal execution and price manipulations in time-varying limit order books," Working Papers hal-00687193, HAL.
    19. Rama Cont & Arseniy Kukanov, 2012. "Optimal order placement in limit order markets," Papers 1210.1625, arXiv.org, revised May 2013.

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