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Three-state herding model of the financial markets

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  • Aleksejus Kononovicius
  • Vygintas Gontis

Abstract

We propose a Markov jump process with the three-state herding interaction. We see our approach as an agent-based model for the financial markets. Under certain assumptions this agent-based model can be related to the stochastic description exhibiting sophisticated statistical features. Along with power-law probability density function of the absolute returns we are able to reproduce the fractured power spectral density, which is observed in the high-frequency financial market data. Given example of consistent agent-based and stochastic modeling will provide background for the further developments in the research of complex social systems.

Suggested Citation

  • Aleksejus Kononovicius & Vygintas Gontis, 2012. "Three-state herding model of the financial markets," Papers 1210.1838, arXiv.org, revised Jan 2013.
    • Handle: RePEc:arx:papers:1210.1838
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    References listed on IDEAS

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    10. Kaulakys, Bronislovas & Ruseckas, Julius & Gontis, Vygintas & Alaburda, Miglius, 2006. "Nonlinear stochastic models of 1/f noise and power-law distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 217-221.
    11. Stefan Bornholdt, 2001. "Expectation Bubbles In A Spin Model Of Markets: Intermittency From Frustration Across Scales," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 12(05), pages 667-674.
    12. 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.
    13. 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.
    14. Gontis, V. & Kaulakys, B. & Ruseckas, J., 2008. "Trading activity as driven Poisson process: Comparison with empirical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3891-3896.
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    Citations

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    Cited by:

    1. Gontis, V. & Havlin, S. & Kononovicius, A. & Podobnik, B. & Stanley, H.E., 2016. "Stochastic model of financial markets reproducing scaling and memory in volatility return intervals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1091-1102.
    2. Aleksejus Kononovicius, 2017. "Empirical Analysis and Agent-Based Modeling of the Lithuanian Parliamentary Elections," Complexity, Hindawi, vol. 2017, pages 1-15, November.
    3. Vygintas Gontis, 2021. "Order flow in the financial markets from the perspective of the Fractional L\'evy stable motion," Papers 2105.02057, arXiv.org, revised Nov 2021.
    4. Ausloos, Marcel, 2021. "Hagiotoponyms in France: Saint popularity, like a herding phase transition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    5. 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.
    6. Vygintas Gontis & Shlomo Havlin & Aleksejus Kononovicius & Boris Podobnik & H. Eugene Stanley, 2015. "Stochastic model of financial markets reproducing scaling and memory in volatility return intervals," Papers 1507.05203, arXiv.org, revised Oct 2016.
    7. Alessio Emanuele Biondo & Alessandro Pluchino & Andrea Rapisarda, 2017. "Informative Contagion Dynamics in a Multilayer Network Model of Financial Markets," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 3(3), pages 343-366, November.
    8. Vygintas Gontis & Aleksejus Kononovicius, 2017. "Spurious memory in non-equilibrium stochastic models of imitative behavior," Papers 1707.09801, arXiv.org.
    9. Aleksejus Kononovicius & Vygintas Gontis, 2014. "Herding interactions as an opportunity to prevent extreme events in financial markets," Papers 1409.8024, arXiv.org, revised May 2015.
    10. Rytis Kazakeviv{c}ius & Aleksejus Kononovicius, 2023. "Anomalous diffusion and long-range memory in the scaled voter model," Papers 2301.08088, arXiv.org, revised Feb 2023.
    11. Gontis, V. & Kononovicius, A., 2017. "Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 483(C), pages 266-272.
    12. Rytis Kazakevicius & Aleksejus Kononovicius & Bronislovas Kaulakys & Vygintas Gontis, 2021. "Understanding the nature of the long-range memory phenomenon in socioeconomic systems," Papers 2108.02506, arXiv.org, revised Aug 2021.
    13. Kononovicius, A. & Gontis, V., 2014. "Control of the socio-economic systems using herding interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 80-84.
    14. V. Gontis & A. Kononovicius, 2017. "Burst and inter-burst duration statistics as empirical test of long-range memory in the financial markets," Papers 1701.01255, arXiv.org.

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