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Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness

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  • Sato, Aki-Hiro
  • Takayasu, Hideki

Abstract

A variant of threshold dynamics is introduced to model the behaviors of a large assembly of dealers in a stock market. Although the microscopic evolution dynamics is deterministic the collective behaviors such as market prices show seemingly stochastic fluctuations. The statistical properties of market price change can be well approximated by a simple discrete Langevin-type equation with random amplification. The macroscopic stochastic equation is solved both numerically and analytically showing that the market price change generally follow power-law distributions in the steady state. The reason for the appearance of rapid decay in the distribution tails are discussed.

Suggested Citation

  • Sato, Aki-Hiro & Takayasu, Hideki, 1998. "Dynamic numerical models of stock market price: from microscopic determinism to macroscopic randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 250(1), pages 231-252.
    • Handle: RePEc:eee:phsmap:v:250:y:1998:i:1:p:231-252
    DOI: 10.1016/S0378-4371(97)00569-4
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    Citations

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    Cited by:

    1. Yuki Sato & Kiyoshi Kanazawa, 2023. "Exact solution to a generalised Lillo-Mike-Farmer model with heterogeneous order-splitting strategies," Papers 2306.13378, arXiv.org, revised Nov 2023.
    2. Inoua, Sabiou M. & Smith, Vernon L., 2023. "A classical model of speculative asset price dynamics," Journal of Behavioral and Experimental Finance, Elsevier, vol. 37(C).
    3. Iraj Daizadeh, 2009. "An intellectual property-based corporate strategy: An R&D spend, patent, trademark, media communication, and market price innovation agenda," Scientometrics, Springer;Akadémiai Kiadó, vol. 80(3), pages 731-746, September.
    4. Alberto Ciacci & Takumi Sueshige & Hideki Takayasu & Kim Christensen & Misako Takayasu, 2020. "The microscopic relationships between triangular arbitrage and cross-currency correlations in a simple agent based model of foreign exchange markets," PLOS ONE, Public Library of Science, vol. 15(6), pages 1-19, June.
    5. Murakami, Ryo & Nakamura, Tomomichi & Kimura, Shin & Manabe, Masashi & Tanizawa, Toshihiro, 2015. "On possible origins of trends in financial market price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 179-189.
    6. Lye, Ribin & Tan, James Peng Lung & Cheong, Siew Ann, 2012. "Understanding agent-based models of financial markets: A bottom–up approach based on order parameters and phase diagrams," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5521-5531.
    7. Damien Challet & Tobias Galla, 2005. "Price return autocorrelation and predictability in agent-based models of financial markets," Quantitative Finance, Taylor & Francis Journals, vol. 5(6), pages 569-576.
    8. Tetsuya Takaishi, 2014. "Analysis of Spin Financial Market by GARCH Model," Papers 1409.0118, arXiv.org.
    9. Sornette, Didier & Zhou, Wei-Xing, 2006. "Importance of positive feedbacks and overconfidence in a self-fulfilling Ising model of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 704-726.
    10. H. Takayasu & M. Takayasu & M. P. Okazaki & K. Marumo & T. Shimizu, 2000. "Fractal Properties in Economics," Papers cond-mat/0008057, arXiv.org, revised Aug 2000.
    11. Kiyoshi Kanazawa & Hideki Takayasu & Misako Takayasu, 2022. "Exact solution to two-body financial dealer model: revisited from the viewpoint of kinetic theory," Papers 2205.15558, arXiv.org.
    12. Lux, Thomas & Alfarano, Simone, 2016. "Financial power laws: Empirical evidence, models, and mechanisms," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 3-18.
    13. Aki-Hiro Sato & Hideki Takayasu, 2001. "Market price simulator based on analog electrical circuit," Papers cond-mat/0104318, arXiv.org.
    14. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW Kiel).
    15. Ribin Lye & James Peng Lung Tan & Siew Ann Cheong, 2012. "Understanding agent-based models of financial markets: a bottom-up approach based on order parameters and phase diagrams," Papers 1202.0606, arXiv.org.
    16. Nakamura, Tomomichi & Small, Michael, 2006. "Testing for dynamics in the irregular fluctuations of financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 377-386.
    17. Ryo Murakami & Tomomichi Nakamura & Shin Kimura & Masashi Manabe & Toshihiro Tanizawa, 2014. "On possible origins of trends in financial market price changes," Papers 1406.5276, arXiv.org, revised Nov 2014.
    18. Sabiou M. Inoua, 2020. "News-Driven Expectations and Volatility Clustering," JRFM, MDPI, vol. 13(1), pages 1-14, January.
    19. Mathieu, Philippe & Morvan, Rémi, 2019. "A deterministic behaviour for realistic price dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 33-49.
    20. Sabiou Inoua, 2016. "Speculation and Power Law," Papers 1612.08705, arXiv.org.
    21. Lux, Thomas, 2006. "Financial power laws: Empirical evidence, models, and mechanism," Economics Working Papers 2006-12, Christian-Albrechts-University of Kiel, Department of Economics.
    22. Lee, Chung Kung & Chin Yu, Chung & Cai Wang, Cheng & Der Hwang, Ruey & Kuen Yu, Guey, 2006. "Scaling characteristics in aftershock sequence of earthquake," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(2), pages 692-702.
    23. Aki-Hiro Sato & Hideki Takayasu, 2001. "Derivation of ARCH(1) process from market price changes based on deterministic microscopic multi-agent," Papers cond-mat/0104313, arXiv.org.
    24. Yamasaki, Kazuko & Mackin, Kenneth J., 2003. "The extraction of macromodel and origin of long-ranged correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 417-423.

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