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Optimal trade execution and absence of price manipulations in limit order book models

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  • Aurélien Alfonsi

    ()
    (CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique - Université Paris Est (UPE) - École des Ponts ParisTech (ENPC), MATHRISK - INRIA)

  • Alexander Schied

    (Institute of Mathematics - University of Mannheim)

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    Abstract

    We analyze the existence of price manipulation and optimal trade execution strategies in a model for an electronic limit order book with nonlinear price impact and exponential resilience. Our main results show that, under general conditions on the shape function of the limit order book, placing deterministic trade sizes at trading dates that are homogeneously spaced is optimal within a large class of adaptive strategies with arbitrary trading dates. This extends results from our earlier work with A. Fruth. Perhaps even more importantly, our analysis yields as a corollary that our model does not admit price manipulation strategies. This latter result contrasts the recent findings of Gatheral [12], where, in a related but different model, exponential resilience was found to give rise to price manipulation strategies when price impact is nonlinear.

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    Bibliographic Info

    Paper provided by HAL in its series Post-Print with number hal-00397652.

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    Date of creation: 2010
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    Publication status: Published, SIAM Journal on Financial Mathematics, 2010, 1, 490-522
    Handle: RePEc:hal:journl:hal-00397652

    Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00397652
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    References

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    1. Alexander Schied & Torsten Schöneborn, 2009. "Risk aversion and the dynamics of optimal liquidation strategies in illiquid markets," Finance and Stochastics, Springer, vol. 13(2), pages 181-204, April.
    2. Potters, Marc & Bouchaud, Jean-Philippe, 2003. "More statistical properties of order books and price impact," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 133-140.
    3. Robert Almgren, 2003. "Optimal execution with nonlinear impact functions and trading-enhanced risk," Applied Mathematical Finance, Taylor & Francis Journals, vol. 10(1), pages 1-18.
    4. Bertsimas, Dimitris & Lo, Andrew W., 1998. "Optimal control of execution costs," Journal of Financial Markets, Elsevier, vol. 1(1), pages 1-50, April.
    5. Gur Huberman & Werner Stanzl, 2004. "Price Manipulation and Quasi-Arbitrage," Econometrica, Econometric Society, vol. 72(4), pages 1247-1275, 07.
    6. P. Weber & B. Rosenow, 2005. "Order book approach to price impact," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 357-364.
    7. 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.
    8. Anna Obizhaeva & Jiang Wang, 2005. "Optimal Trading Strategy and Supply/Demand Dynamics," NBER Working Papers 11444, National Bureau of Economic Research, Inc.
    9. 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.
    10. Alexander Schied & Torsten Schoneborn & Michael Tehranchi, 2010. "Optimal Basket Liquidation for CARA Investors is Deterministic," Applied Mathematical Finance, Taylor & Francis Journals, vol. 17(6), pages 471-489.
    11. Jean-Philippe Bouchaud & Yuval Gefen & Marc Potters & Matthieu Wyart, 2003. "Fluctuations and response in financial markets: the subtle nature of `random' price changes," Papers cond-mat/0307332, arXiv.org, revised Aug 2003.
    12. 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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    Citations

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    Cited by:
    1. Aurélien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Working Papers hal-00971369, HAL.
    2. Samuel N. Cohen & Lukasz Szpruch, 2011. "A limit order book model for latency arbitrage," Papers 1110.4811, arXiv.org.
    3. Takashi Kato, 2011. "An Optimal Execution Problem in Geometric Ornstein-Uhlenbeck Price Process," Papers 1107.1787, arXiv.org, revised Jul 2014.
    4. Alexander Schied & Tao Zhang, 2013. "A hot-potato game under transient price impact and some effects of a transaction tax," Papers 1305.4013, arXiv.org, revised Sep 2013.
    5. Christopher Lorenz & Alexander Schied, 2013. "Drift dependence of optimal trade execution strategies under transient price impact," Finance and Stochastics, Springer, vol. 17(4), pages 743-770, October.
    6. Aur\'elien Alfonsi & Alexander Schied & Florian Kl\"ock, 2013. "Multivariate transient price impact and matrix-valued positive definite functions," Papers 1310.4471, arXiv.org, revised May 2014.
    7. Aur\'elien Alfonsi & Jos\'e Infante Acevedo, 2012. "Optimal execution and price manipulations in time-varying limit order books," Papers 1204.2736, arXiv.org.
    8. Aurélien Alfonsi & José Infante Acevedo, 2012. "Optimal execution and price manipulations in time-varying limit order books," Working Papers hal-00687193, HAL.
    9. Olivier Gu\'eant & Charles-Albert Lehalle, 2012. "General Intensity Shapes in Optimal Liquidation," Papers 1204.0148, arXiv.org, revised Jun 2013.
    10. Aurélien Alfonsi & Alexander Schied, 2013. "Capacitary measures for completely monotone kernels via singular control," Post-Print hal-00659421, HAL.
    11. Olivier Gu\'eant, 2013. "Permanent market impact can be nonlinear," Papers 1305.0413, arXiv.org, revised Mar 2014.
    12. Aur\'elien Alfonsi & Pierre Blanc, 2014. "Dynamic optimal execution in a mixed-market-impact Hawkes price model," Papers 1404.0648, arXiv.org.
    13. Erhan Bayraktar & Michael Ludkovski, 2011. "Liquidation in Limit Order Books with Controlled Intensity," Papers 1105.0247, arXiv.org, revised Jan 2012.
    14. Kühn, Christoph & Stroh, Maximilian, 2013. "Continuous time trading of a small investor in a limit order market," Stochastic Processes and their Applications, Elsevier, vol. 123(6), pages 2011-2053.
    15. Charles-Albert Lehalle, 2013. "Market Microstructure Knowledge Needed for Controlling an Intra-Day Trading Process," Papers 1302.4592, arXiv.org.
    16. Qinghua Li, 2014. "Facilitation and Internalization Optimal Strategy in a Multilateral Trading Context," Papers 1404.7320, arXiv.org.
    17. Florian Kl\"ock & Alexander Schied & Yuemeng Sun, 2012. "Price manipulation in a market impact model with dark pool," Papers 1205.4008, arXiv.org, revised May 2014.
    18. Olivier Gu\'eant & Charles-Albert Lehalle & Joaquin Fernandez Tapia, 2011. "Dealing with the Inventory Risk. A solution to the market making problem," Papers 1105.3115, arXiv.org, revised Aug 2012.

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