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Simulations Of Financial Markets In A Potts-Like Model

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  • TETSUYA TAKAISHI

    (CERN, Physics Department, TH Unit, CH-1211 Genève 23, Switzerland;
    Hiroshima University of Economics, Hiroshima 731-0124, Japan)

Abstract

A three-state model based on the Potts model is proposed to simulate financial markets. The three states are assigned to "buy", "sell" and "inactive" states. The model shows the main stylized facts observed in the financial market: fat-tailed distributions of returns and long time correlations in the absolute returns. At low inactivity rate, the model effectively reduces to the two-state model of Bornholdt and shows similar results to the Bornholdt model. As the inactivity increases, we observe the exponential distributions of returns.

Suggested Citation

  • Tetsuya Takaishi, 2005. "Simulations Of Financial Markets In A Potts-Like Model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 16(08), pages 1311-1317.
    • Handle: RePEc:wsi:ijmpcx:v:16:y:2005:i:08:n:s0129183105007923
    DOI: 10.1142/S0129183105007923
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, November.
    2. Perez, A.A, 2001. "Comment on “On the multinomial logic model” [Physica A 269 (1999) 9–15]," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 289(3), pages 606-606.
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    Citations

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    Cited by:

    1. Tetsuya Takaishi, 2016. "Dynamical cross-correlation of multiple time series Ising model," Evolutionary and Institutional Economics Review, Springer, vol. 13(2), pages 455-468, December.
    2. Bornholdt, Stefan, 2022. "A q-spin Potts model of markets: Gain–loss asymmetry in stock indices as an emergent phenomenon," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    3. Zubillaga, Bernardo J. & Vilela, André L.M. & Wang, Chao & Nelson, Kenric P. & Stanley, H. Eugene, 2022. "A three-state opinion formation model for financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    4. Tetsuya Takaishi, 2009. "An Adaptive Markov Chain Monte Carlo Method for GARCH Model," Papers 0901.0992, arXiv.org.
    5. Stefan Bornholdt, 2021. "A q-spin Potts model of markets: Gain-loss asymmetry in stock indices as an emergent phenomenon," Papers 2112.06290, arXiv.org.
    6. Tetsuya Takaishi, 2008. "Financial Time Series Analysis of SV Model by Hybrid Monte Carlo," Papers 0807.4394, arXiv.org.
    7. Tetsuya Takaishi, 2014. "Analysis of Spin Financial Market by GARCH Model," Papers 1409.0118, arXiv.org.

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