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Order book model with herd behavior exhibiting long-range memory

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  • Kononovicius, Aleksejus
  • Ruseckas, Julius

Abstract

In this work, we propose an order book model with herd behavior. The proposed model is built upon two distinct approaches: a recent empirical study of the detailed order book records by Kanazawa et al. (2018) and financial herd behavior model. Combining these approaches allows us to propose a model that replicates the long-range memory of absolute return and trading activity. We compare the statistical properties of the model against the empirical statistical properties of the Bitcoin exchange rates and New York stock exchange tickers. We also show that the fracture in the spectral density of the high-frequency absolute return time series might be related to the mechanism of convergence towards the equilibrium price.

Suggested Citation

  • Kononovicius, Aleksejus & Ruseckas, Julius, 2019. "Order book model with herd behavior exhibiting long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 171-191.
    • Handle: RePEc:eee:phsmap:v:525:y:2019:i:c:p:171-191
    DOI: 10.1016/j.physa.2019.03.059
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    as
    1. Luisanna Cocco & Giulio Concas & Michele Marchesi, 2017. "Using an artificial financial market for studying a cryptocurrency market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(2), pages 345-365, July.
    2. Nax, Heinrich H. & Pradelski, Bary S. R., 2015. "Evolutionary dynamics and equitable core selection in assignment games," LSE Research Online Documents on Economics 65428, London School of Economics and Political Science, LSE Library.
    3. T. T. Chen & B. Zheng & Y. Li & X. F. Jiang, 2017. "New approaches in agent-based modeling of complex financial systems," Papers 1703.06840, arXiv.org.
    4. Dirk Helbing, "undated". "Pluralistic Modeling of Complex Systems," Working Papers CCSS-10-009, ETH Zurich, Chair of Systems Design.
    5. Eric Smith & J Doyne Farmer & Laszlo Gillemot & Supriya Krishnamurthy, 2003. "Statistical theory of the continuous double auction," Quantitative Finance, Taylor & Francis Journals, vol. 3(6), pages 481-514.
    6. M. Cristelli & V. Alfi & L. Pietronero & A. Zaccaria, 2010. "Liquidity crisis, granularity of the order book and price fluctuations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 73(1), pages 41-49, January.
    7. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    8. Aleksejus Kononovicius & Julius Ruseckas, 2014. "Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 87(8), pages 1-7, August.
    9. Aleksejus Kononovicius, 2017. "Empirical Analysis and Agent-Based Modeling of the Lithuanian Parliamentary Elections," Complexity, Hindawi, vol. 2017, pages 1-15, November.
    10. Thomas Lux & Michele Marchesi, 1999. "Scaling and criticality in a stochastic multi-agent model of a financial market," Nature, Nature, vol. 397(6719), pages 498-500, February.
    11. D. Sornette, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based models," Papers 1404.0243, arXiv.org.
    12. Kaizoji, Taisei & Leiss, Matthias & Saichev, Alexander & Sornette, Didier, 2015. "Super-exponential endogenous bubbles in an equilibrium model of fundamentalist and chartist traders," Journal of Economic Behavior & Organization, Elsevier, vol. 112(C), pages 289-310.
    13. repec:sae:jocore:v:55:y:2011:i:6:p:970-955 is not listed on IDEAS
    14. V. Gontis & A. Kononovicius, 2014. "Consentaneous agent-based and stochastic model of the financial markets," Papers 1403.1574, arXiv.org, revised Jul 2014.
    15. Alan Kirman, 1993. "Ants, Rationality, and Recruitment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(1), pages 137-156.
    16. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Quantitative Finance, Taylor & Francis Journals, vol. 2(4), pages 251-256.
    17. Challet, Damien & Stinchcombe, Robin, 2001. "Analyzing and modeling 1+1d markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 300(1), pages 285-299.
    18. Vernon L. Smith, 1962. "An Experimental Study of Competitive Market Behavior," Journal of Political Economy, University of Chicago Press, vol. 70, pages 111-111.
    19. Vygintas Gontis & Aleksejus Kononovicius, 2014. "Consentaneous Agent-Based and Stochastic Model of the Financial Markets," PLOS ONE, Public Library of Science, vol. 9(7), pages 1-12, July.
    20. Kononovicius, A. & Gontis, V., 2012. "Agent based reasoning for the non-linear stochastic models of long-range memory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1309-1314.
    21. Roberto Mota Navarro & Hernán Larralde, 2017. "A detailed heterogeneous agent model for a single asset financial market with trading via an order book," PLOS ONE, Public Library of Science, vol. 12(2), pages 1-27, February.
    22. Stanis{l}aw Dro.zd.z & Robert Gk{e}barowski & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marcin Wk{a}torek, 2018. "Bitcoin market route to maturity? Evidence from return fluctuations, temporal correlations and multiscaling effects," Papers 1804.05916, arXiv.org, revised Jul 2018.
    23. Didier SORNETTE, 2014. "Physics and Financial Economics (1776-2014): Puzzles, Ising and Agent-Based Models," Swiss Finance Institute Research Paper Series 14-25, Swiss Finance Institute.
    24. Parameswaran Gopikrishnan & Vasiliki Plerou & Xavier Gabaix & H. Eugene Stanley, 2000. "Statistical Properties of Share Volume Traded in Financial Markets," Papers cond-mat/0008113, arXiv.org.
    25. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    26. Alfarano, Simone & Lux, Thomas & Wagner, Friedrich, 2008. "Time variation of higher moments in a financial market with heterogeneous agents: An analytical approach," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 101-136, January.
    27. Heinrich Nax & Bary Pradelski, 2015. "Evolutionary dynamics and equitable core selection in assignment games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 903-932, November.
    28. Rafal Rak & Stanislaw Drozdz & Jaroslaw Kwapien & Pawel Oswiecimka, 2013. "Stock returns versus trading volume: is the correspondence more general?," Papers 1310.7018, arXiv.org.
    29. Alessio Emanuele Biondo, 2018. "Order book microstructure and policies for financial stability," Studies in Economics and Finance, Emerald Group Publishing Limited, vol. 35(1), pages 196-218, March.
    30. Bayati, Mohsen & Borgs, Christian & Chayes, Jennifer & Kanoria, Yash & Montanari, Andrea, 2015. "Bargaining dynamics in exchange networks," Journal of Economic Theory, Elsevier, vol. 156(C), pages 417-454.
    31. Stjepan Beguv{s}i'c & Zvonko Kostanjv{c}ar & H. Eugene Stanley & Boris Podobnik, 2018. "Scaling properties of extreme price fluctuations in Bitcoin markets," Papers 1803.08405, arXiv.org.
    32. Bak, P. & Paczuski, M. & Shubik, M., 1997. "Price variations in a stock market with many agents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 246(3), pages 430-453.
    33. Biais, Bruno & Hillion, Pierre & Spatt, Chester, 1995. "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," Journal of Finance, American Finance Association, vol. 50(5), pages 1655-1689, December.
    34. Jean-Philippe Bouchaud & Marc Mezard & Marc Potters, 2002. "Statistical properties of stock order books: empirical results and models," Science & Finance (CFM) working paper archive 0203511, Science & Finance, Capital Fund Management.
    35. Lux, Thomas, 2018. "Estimation of agent-based models using sequential Monte Carlo methods," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 391-408.
    36. V. Alfi & M. Cristelli & L. Pietronero & A. Zaccaria, 2009. "Minimal agent based model for financial markets I," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 67(3), pages 385-397, February.
    37. Simone Alfarano & Thomas Lux & Friedrich Wagner, 2005. "Estimation of Agent-Based Models: The Case of an Asymmetric Herding Model," Computational Economics, Springer;Society for Computational Economics, vol. 26(1), pages 19-49, August.
    38. Alfarano, Simone & Milakovic, Mishael, 2009. "Network structure and N-dependence in agent-based herding models," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 78-92, January.
    39. Aleksejus Kononovicius & Vygintas Gontis & Valentas Daniunas, 2012. "Agent-based Versus Macroscopic Modeling of Competition and Business Processes in Economics and Finance," Papers 1202.3533, arXiv.org, revised Jun 2012.
    40. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    41. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach To Order Book Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-40.
    42. Biondo, Alessio Emanuele, 2018. "Learning to forecast, risk aversion, and microstructural aspects of financial stability," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 12, pages 1-21.
    43. Bàrbara Llacay & Gilbert Peffer, 2018. "Using realistic trading strategies in an agent-based stock market model," Computational and Mathematical Organization Theory, Springer, vol. 24(3), pages 308-350, September.
    44. R. Cont, 2001. "Empirical properties of asset returns: stylized facts and statistical issues," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 223-236.
    45. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    46. Begušić, Stjepan & Kostanjčar, Zvonko & Eugene Stanley, H. & Podobnik, Boris, 2018. "Scaling properties of extreme price fluctuations in Bitcoin markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 400-406.
    47. Andreas Flache & Michael Mäs & Thomas Feliciani & Edmund Chattoe-Brown & Guillaume Deffuant & Sylvie Huet & Jan Lorenz, 2017. "Models of Social Influence: Towards the Next Frontiers," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 20(4), pages 1-2.
    48. Maslov, Sergei, 2000. "Simple model of a limit order-driven market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(3), pages 571-578.
    49. Julius Ruseckas & Vygintas Gontis & Bronislovas Kaulakys, 2012. "Nonextensive Statistical Mechanics Distributions And Dynamics Of Financial Observables From The Nonlinear Stochastic Differential Equations," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 15(supp0), pages 1-13.
    50. Kimbrough, Erik O. & Smyth, Andrew, 2018. "Testing the boundaries of the double auction: The effects of complete information and market power," Journal of Economic Behavior & Organization, Elsevier, vol. 150(C), pages 372-396.
    51. Frédéric Abergel & Aymen Jedidi, 2013. "A Mathematical Approach to Order Book Modelling," Post-Print hal-00621253, HAL.
    52. Kiyoshi Kanazawa & Takumi Sueshige & Hideki Takayasu & Misako Takayasu, 2018. "Kinetic Theory for Finance Brownian Motion from Microscopic Dynamics," Papers 1802.05993, arXiv.org.
    53. Frederic Abergel & Aymen Jedidi, 2010. "A Mathematical Approach to Order Book Modeling," Papers 1010.5136, arXiv.org, revised Mar 2013.
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