IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i10p2348-d1149776.html
   My bibliography  Save this article

Coexisting Attractors in a Heterogeneous Agent Model in Discrete Time

Author

Listed:
  • Serena Brianzoni

    (Department of Management, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy
    These authors contributed equally to this work.)

  • Giovanni Campisi

    (Department of Management, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy
    These authors contributed equally to this work.)

  • Graziella Pacelli

    (Department of Management, Polytechnic University of Marche, Piazzale Martelli 8, 60121 Ancona, Italy
    These authors contributed equally to this work.)

Abstract

In this paper, the discrete-time version of a continuous-time model with fundamentalists and momentum traders is presented. Our aim consists of studying the impact of cross-sectional momentum traders on the dynamics of the model. To this end, the continuous-time deterministic skeleton of the benchmark model is transformed using sophisticated discretization techniques. It is worth noting that the model does not always maintain the same characteristics after moving from continuous to discrete time. In spite of this, our discrete-time system preserves the dynamic properties of the continuous-time original model. Moreover, heterogeneity introduces an important non-linearity into the market dynamics, causing our deterministic financial model to generate erratic time series similar to the patterns observed in real markets. In particular, we show that the time series originated by the perturbed deterministic system capture some of the main stylized facts of the U.S. financial market. Converting the benchmark model from continuous time to discrete time allows the use of financial data available in discrete time.

Suggested Citation

  • Serena Brianzoni & Giovanni Campisi & Graziella Pacelli, 2023. "Coexisting Attractors in a Heterogeneous Agent Model in Discrete Time," Mathematics, MDPI, vol. 11(10), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2348-:d:1149776
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/10/2348/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/10/2348/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Xue-Zhong He & Kai Li & Chuncheng Wang, 2018. "Time-varying economic dominance in financial markets: A bistable dynamics approach," Published Paper Series 2018-1, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    2. He, Xue-Zhong & Zheng, Huanhuan, 2016. "Trading heterogeneity under information uncertainty," Journal of Economic Behavior & Organization, Elsevier, vol. 130(C), pages 64-80.
    3. Fabio Tramontana & Laura Gardini & Roberto Dieci & Frank Westerhoff, 2009. "The Emergence of Bull and Bear Dynamics in a Nonlinear Model of Interacting Markets," Discrete Dynamics in Nature and Society, Hindawi, vol. 2009, pages 1-30, July.
    4. Westerhoff, Frank H. & Dieci, Roberto, 2006. "The effectiveness of Keynes-Tobin transaction taxes when heterogeneous agents can trade in different markets: A behavioral finance approach," Journal of Economic Dynamics and Control, Elsevier, vol. 30(2), pages 293-322, February.
    5. Grassetti, F. & Guzowska, M. & Michetti, E., 2020. "A dynamically consistent discretization method for Goodwin model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    6. Brock, William A. & Hommes, Cars H., 1998. "Heterogeneous beliefs and routes to chaos in a simple asset pricing model," Journal of Economic Dynamics and Control, Elsevier, vol. 22(8-9), pages 1235-1274, August.
    7. Lux, Thomas, 1998. "The socio-economic dynamics of speculative markets: interacting agents, chaos, and the fat tails of return distributions," Journal of Economic Behavior & Organization, Elsevier, vol. 33(2), pages 143-165, January.
    8. Kukacka, Jiri & Barunik, Jozef, 2017. "Estimation of financial agent-based models with simulated maximum likelihood," Journal of Economic Dynamics and Control, Elsevier, vol. 85(C), pages 21-45.
    9. Carl Chiarella & Giulia Iori, 2002. "A simulation analysis of the microstructure of double auction markets," Quantitative Finance, Taylor & Francis Journals, vol. 2(5), pages 346-353.
    10. Serena Brianzoni & Cristiana Mammana & Elisabetta Michetti, 2010. "Updating Wealth in an Asset Pricing Model with Heterogeneous Agents," Discrete Dynamics in Nature and Society, Hindawi, vol. 2010, pages 1-27, November.
    11. Roberto Dieci & Xue-Zhong He, 2021. "Cross-section instability in financial markets: impatience, extrapolation, and switching," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(2), pages 727-754, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Changtai Li & Weihong Huang & Wei-Siang Wang & Wai-Mun Chia, 2023. "Price Change and Trading Volume: Behavioral Heterogeneity in Stock Market," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 677-713, February.
    2. Frank H. Westerhoff, 2009. "Exchange Rate Dynamics: A Nonlinear Survey," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 11, Edward Elgar Publishing.
    3. Giorgio Fagiolo & Mattia Guerini & Francesco Lamperti & Alessio Moneta & Andrea Roventini, 2017. "Validation of Agent-Based Models in Economics and Finance," LEM Papers Series 2017/23, Laboratory of Economics and Management (LEM), Sant'Anna School of Advanced Studies, Pisa, Italy.
    4. Frijns, Bart & Lehnert, Thorsten & Zwinkels, Remco C.J., 2010. "Behavioral heterogeneity in the option market," Journal of Economic Dynamics and Control, Elsevier, vol. 34(11), pages 2273-2287, November.
    5. Zhenxi Chen & Weihong Huang & Huanhuan Zheng, 2018. "Estimating heterogeneous agents behavior in a two-market financial system," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 13(3), pages 491-510, October.
    6. J. Doyne Farmer & John Geanakoplos, 2008. "The virtues and vices of equilibrium and the future of financial economics," Papers 0803.2996, arXiv.org.
    7. He, Xue-Zhong & Li, Youwei, 2015. "Testing of a market fraction model and power-law behaviour in the DAX 30," Journal of Empirical Finance, Elsevier, vol. 31(C), pages 1-17.
    8. Cafferata, Alessia & Tramontana, Fabio, 2019. "A financial market model with confirmation bias," Structural Change and Economic Dynamics, Elsevier, vol. 51(C), pages 252-259.
    9. Dieci, Roberto & Westerhoff, Frank, 2010. "Heterogeneous speculators, endogenous fluctuations and interacting markets: A model of stock prices and exchange rates," Journal of Economic Dynamics and Control, Elsevier, vol. 34(4), pages 743-764, April.
    10. 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.
    11. He, Xue-Zhong & Li, Youwei, 2007. "Power-law behaviour, heterogeneity, and trend chasing," Journal of Economic Dynamics and Control, Elsevier, vol. 31(10), pages 3396-3426, October.
    12. Bauer, Christian & De Grauwe, Paul & Reitz, Stefan, 2009. "Exchange rate dynamics in a target zone--A heterogeneous expectations approach," Journal of Economic Dynamics and Control, Elsevier, vol. 33(2), pages 329-344, February.
    13. Alexandru Mandes & Peter Winker, 2017. "Complexity and model comparison in agent based modeling of financial markets," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(3), pages 469-506, October.
    14. Giovanni Campisi & Silvia Muzzioli, 2020. "Investor sentiment and trading behavior," Department of Economics 0163, University of Modena and Reggio E., Faculty of Economics "Marco Biagi".
    15. Huang, Weihong & Chen, Zhenxi, 2014. "Modeling regional linkage of financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 99(C), pages 18-31.
    16. Jawadi, Fredj & Namouri, Hela & Ftiti, Zied, 2018. "An analysis of the effect of investor sentiment in a heterogeneous switching transition model for G7 stock markets," Journal of Economic Dynamics and Control, Elsevier, vol. 91(C), pages 469-484.
    17. Biondo, Alessio Emanuele, 2017. "Learning to forecast, risk aversion, and microstructural aspects of financial stability," Economics Discussion Papers 2017-104, Kiel Institute for the World Economy (IfW Kiel).
    18. Youwei Li & Bas Donkers & Bertrand Melenberg, 2010. "Econometric analysis of microscopic simulation models," Quantitative Finance, Taylor & Francis Journals, vol. 10(10), pages 1187-1201.
    19. Baumann, Michael Heinrich & Baumann, Michaela & Erler, Alexander, 2019. "Limitations of stabilizing effects of fundamentalists: Facing positive feedback traders," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 13, pages 1-26.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:11:y:2023:i:10:p:2348-:d:1149776. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.