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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
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    References listed on IDEAS

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    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. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Grassetti, F. & Guzowska, M. & Michetti, E., 2020. "A dynamically consistent discretization method for Goodwin model," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    10. 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.
    11. 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.
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