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Mean-field approximation for a limit order driven market model

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  • Frantisek Slanina

Abstract

The mean-field variant of the model of limit order driven market introduced recently by Maslov is formulated and solved. The agents do not have any strategies and the memory of the system is kept within the order book. We show that he evolution of the order book is governed by a matrix multiplicative process. The resulting stationary distribution of step-to-step price changes is calculated. It exhibits a power-law tail with exponent 2. We obtain also the price autocorrelation function, which agrees qualitatively with the experimentally observed negative autocorrelation for short times.

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  • Frantisek Slanina, 2001. "Mean-field approximation for a limit order driven market model," Papers cond-mat/0104547, arXiv.org, revised Aug 2001.
    • Handle: RePEc:arx:papers:cond-mat/0104547
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    Cited by:

    1. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    2. 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.
    3. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    4. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    5. 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.
    6. Jovanovic, Franck & Schinckus, Christophe, 2017. "Econophysics and Financial Economics: An Emerging Dialogue," OUP Catalogue, Oxford University Press, number 9780190205034.
    7. Kostanjcar, Zvonko & Jeren, Branko & Juretic, Zeljan, 2012. "Impact of uncertainty in expected return estimation on stock price volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5563-5571.
    8. Tingqiang Chen & Binqing Xiao & Haifei Liu, 2018. "Credit Risk Contagion in an Evolving Network Model Integrating Spillover Effects and Behavioral Interventions," Complexity, Hindawi, vol. 2018, pages 1-16, March.
    9. 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.
    10. Biondi, Yuri & Giannoccolo, Pierpaolo & Galam, Serge, 2012. "Formation of share market prices under heterogeneous beliefs and common knowledge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5532-5545.
    11. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    12. Jean-Philippe Bouchaud & J. Doyne Farmer & Fabrizio Lillo, 2008. "How markets slowly digest changes in supply and demand," Papers 0809.0822, arXiv.org.
    13. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    14. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 9, Edward Elgar Publishing.
    15. Maskawa, Jun-ichi, 2007. "Stock price fluctuations and the mimetic behaviors of traders," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 172-178.
    16. Withanawasam, R.M. & Whigham, P.A. & Crack, Timothy Falcon, 2013. "Characterizing limit order prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(21), pages 5346-5355.
    17. 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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