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Impact of meta-order in the Minority Game

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  • Andre Cardoso Barato
  • Iacopo Mastromatteo
  • Marco Bardoscia
  • Matteo Marsili
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    Abstract

    We study the market impact of a meta-order in the framework of the Minority Game. This amounts to studying the response of the market when introducing a trader who buys or sells a fixed amount h for a finite time T. This perturbation introduces statistical arbitrages that traders exploit by adapting their trading strategies. The market impact depends on the nature of the stationary state: We find that the permanent impact is zero in the unpredictable (information efficient) phase, while in the predictable phase it is non-zero and grows linearly with the size of the meta-order. This establishes a quantitative link between information efficiency and trading efficiency (i.e. market impact). By using statistical mechanics methods for disordered systems, we are able to fully characterize the response in the predictable phase, to relate execution cost to response functions and obtain exact results for the permanent impact.

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    File URL: http://arxiv.org/pdf/1112.3908
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1112.3908.

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    Date of creation: Dec 2011
    Date of revision: Nov 2012
    Publication status: Published in Quantitative Finance 13-9 (2013), pp. 1343-1352
    Handle: RePEc:arx:papers:1112.3908

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    1. Vasiliki Plerou & Parameswaran Gopikrishnan & Xavier Gabaix & H. Eugene Stanley, 2001. "Quantifying Stock Price Response to Demand Fluctuations," Papers cond-mat/0106657, arXiv.org.
    2. Marsili, Matteo, 2001. "Market mechanism and expectations in minority and majority games," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 93-103.
    3. Iacopo Mastromatteo & Matteo Marsili & Patrick Zoi, 2010. "Financial correlations at ultra-high frequency: theoretical models and empirical estimation," Papers 1011.1011, arXiv.org, revised Feb 2011.
    4. Esteban Moro & Javier Vicente & Luis G. Moyano & Austin Gerig & J. Doyne Farmer & Gabriella Vaglica & Fabrizio Lillo & Rosario N. Mantegna, 2009. "Market impact and trading profile of large trading orders in stock markets," Papers 0908.0202, arXiv.org.
    5. D. Challet & A. Chessa & M. Marsili & Y. -C. Zhang, 2000. "From Minority Games to real markets," Papers cond-mat/0011042, arXiv.org.
    6. Lawrence R. Glosten & Paul R. Milgrom, 1983. "Bid, Ask and Transaction Prices in a Specialist Market with Heterogeneously Informed Traders," Discussion Papers 570, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Damien Challet & Matteo Marsili, 2002. "Criticality and finite size effects in a simple realistic model of stock market," Papers cond-mat/0210549, arXiv.org, revised Dec 2002.
    8. Hasbrouck, Joel, 1991. " Measuring the Information Content of Stock Trades," Journal of Finance, American Finance Association, vol. 46(1), pages 179-207, March.
    9. J. Doyne Farmer & Austin Gerig & Fabrizio Lillo & Henri Waelbroeck, 2011. "How efficiency shapes market impact," Papers 1102.5457, arXiv.org, revised Sep 2013.
    10. Kyle, Albert S, 1985. "Continuous Auctions and Insider Trading," Econometrica, Econometric Society, vol. 53(6), pages 1315-35, November.
    11. J. Doyne Farmer & Paolo Patelli & Ilija I. Zovko, 2003. "The Predictive Power of Zero Intelligence in Financial Markets," Papers cond-mat/0309233, arXiv.org, revised Feb 2004.
    12. Challet, D. & Zhang, Y.-C., 1997. "Emergence of cooperation and organization in an evolutionary game," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 407-418.
    13. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    14. I. Mastromatteo & M. Marsili & P. Zoi, 2011. "Financial correlations at ultra-high frequency: theoretical models and empirical estimation," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 80(2), pages 243-253, March.
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