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Simple agent-based dynamical system models for efficient financial markets: Theory and examples

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  • Immonen, Eero

Abstract

We propose an agent-based framework, based on simple piecewise linear time-invariant continuous-time dynamical systems models, as a means for describing efficient financial markets. We show by examples that many of the common agent-specific trading strategies occurring in the academic literature, including chartists and fundamentalists of various kinds, can be described in the proposed framework. We present definitions for weak and strong market efficiency and provide necessary and sufficient conditions for them to hold. We present minimal examples of strongly and weakly efficient markets to show that these concepts are natural and easy to satisfy in agent-based models, and that the models can reproduce both statistical and behavioral stylized facts of real markets. We provide examples to demonstrate that the framework can be extended for agents with delays in information processing, as well as for agents with time-varying strategies and for nonlinear market impact functions. We also provide a counterexample to show that the proposed market efficiency concepts may require modification in generalizations for nonlinear trading strategies.

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  • Immonen, Eero, 2017. "Simple agent-based dynamical system models for efficient financial markets: Theory and examples," Journal of Mathematical Economics, Elsevier, vol. 69(C), pages 38-53.
    • Handle: RePEc:eee:mateco:v:69:y:2017:i:c:p:38-53
    DOI: 10.1016/j.jmateco.2016.12.005
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    as
    1. Calvet, Laurent E. & Fisher, Adlai J., 2008. "Multifrequency jump-diffusions: An equilibrium approach," Journal of Mathematical Economics, Elsevier, vol. 44(2), pages 207-226, January.
    2. 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.
    3. Barberis, Nicholas & Greenwood, Robin & Jin, Lawrence & Shleifer, Andrei, 2015. "X-CAPM: An extrapolative capital asset pricing model," Journal of Financial Economics, Elsevier, vol. 115(1), pages 1-24.
    4. Boubaker, Sabri & Farag, Hisham & Nguyen, Duc Khuong, 2015. "Short-term overreaction to specific events: Evidence from an emerging market," Research in International Business and Finance, Elsevier, vol. 35(C), pages 153-165.
    5. Gavious, Arieh & Kedar-Levy, Haim, 2013. "The speed of stock price discovery," Journal of Financial Intermediation, Elsevier, vol. 22(2), pages 245-258.
    6. LeBaron, Blake, 2006. "Agent-based Computational Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 24, pages 1187-1233, Elsevier.
    7. De Long, J Bradford, et al, 1990. "Positive Feedback Investment Strategies and Destabilizing Rational Speculation," Journal of Finance, American Finance Association, vol. 45(2), pages 379-395, June.
    8. Leigh Tesfatsion & Kenneth L. Judd (ed.), 2006. "Handbook of Computational Economics," Handbook of Computational Economics, Elsevier, edition 1, volume 2, number 2.
    9. Alvarez-Ramirez, Jose & Suarez, Rodolfo & Ibarra-Valdez, Carlos, 2003. "Trading strategies, feedback control and market dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 220-226.
    10. Fama, Eugene F, 1970. "Efficient Capital Markets: A Review of Theory and Empirical Work," Journal of Finance, American Finance Association, vol. 25(2), pages 383-417, May.
    11. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: II. Agent-based models," Post-Print hal-00621059, HAL.
    12. Hommes, Cars H., 2006. "Heterogeneous Agent Models in Economics and Finance," Handbook of Computational Economics, in: Leigh Tesfatsion & Kenneth L. Judd (ed.), Handbook of Computational Economics, edition 1, volume 2, chapter 23, pages 1109-1186, Elsevier.
    13. Thomas Lux & Michele Marchesi, 2000. "Volatility Clustering In Financial Markets: A Microsimulation Of Interacting Agents," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 675-702.
    14. Bernard, Vl & Thomas, Jk, 1989. "Post-Earnings-Announcement Drift - Delayed Price Response Or Risk Premium," Journal of Accounting Research, Wiley Blackwell, vol. 27, pages 1-36.
    15. Immonen, Eero, 2015. "A quantitative description for efficient financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 433(C), pages 171-181.
    16. C. Schinckus, 2012. "Methodological comment on Econophysics review I and II: statistical econophysics and agent-based econophysics," Quantitative Finance, Taylor & Francis Journals, vol. 12(8), pages 1189-1192, June.
    17. J. Doyne Farmer & Duncan Foley, 2009. "The economy needs agent-based modelling," Nature, Nature, vol. 460(7256), pages 685-686, August.
    18. Chiarella, Carl & He, Xue-Zhong & Zwinkels, Remco C.J., 2014. "Heterogeneous expectations in asset pricing: Empirical evidence from the S&P500," Journal of Economic Behavior & Organization, Elsevier, vol. 105(C), pages 1-16.
    19. 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.
    20. Simone Bianco & Roberto Renò, 2006. "Dynamics of intraday serial correlation in the Italian futures market," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 26(1), pages 61-84, January.
    21. 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.
    22. Fabrizio Lillo & J. Doyne Farmer & Rosario N. Mantegna, 2003. "Master curve for price-impact function," Nature, Nature, vol. 421(6919), pages 129-130, January.
    23. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    24. Asparouhova, Elena & Bossaerts, Peter & Plott, Charles, 2003. "Excess demand and equilibration in multi-security financial markets: the empirical evidence," Journal of Financial Markets, Elsevier, vol. 6(1), pages 1-21, January.
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    2. Yue Chen & Xiaojian Niu & Yan Zhang, 2019. "Exploring Contrarian Degree in the Trading Behavior of China's Stock Market," Complexity, Hindawi, vol. 2019, pages 1-12, April.

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