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Reaction–diffusion–branching models of stock price fluctuations

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  • Tang, Lei-Han
  • Tian, Guang-Shan

Abstract

Several models of stock trading (Bak et al., Physica A 246 (1997) 430.) are analyzed in analogy with one-dimensional, two-species reaction–diffusion–branching processes. Using heuristic and scaling arguments, we show that the short-time market price variation is subdiffusive with a Hurst exponent H=1/4. Biased diffusion towards the market price and blind-eyed copying lead to crossovers to the empirically observed random-walk behavior (H=1/2) at long times. The calculated crossover forms and diffusion constants are shown to agree well with simulation data.

Suggested Citation

  • Tang, Lei-Han & Tian, Guang-Shan, 1999. "Reaction–diffusion–branching models of stock price fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 543-550.
    • Handle: RePEc:eee:phsmap:v:264:y:1999:i:3:p:543-550
    DOI: 10.1016/S0378-4371(98)00549-4
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    References listed on IDEAS

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    1. Wilmott,Paul & Howison,Sam & Dewynne,Jeff, 1995. "The Mathematics of Financial Derivatives," Cambridge Books, Cambridge University Press, number 9780521497893.
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    Cited by:

    1. Mike, Szabolcs & Farmer, J. Doyne, 2008. "An empirical behavioral model of liquidity and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 200-234, January.
    2. Thomas Lux, 2009. "Applications of Statistical Physics in Finance and Economics," Chapters, in: J. Barkley Rosser Jr. (ed.), Handbook of Research on Complexity, chapter 9, Edward Elgar Publishing.
    3. Kyrylo Shmatov & Mikhail Smirnov, 2005. "On Some Processes and Distributions in a Collective Model of Investors' Behavior," Papers nlin/0506015, arXiv.org.
    4. Anton Bovier & Jiří Černý & Ostap Hryniv, 2006. "The Opinion Game: Stock Price Evolution From Microscopic Market Modeling," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 91-111.
    5. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW Kiel).
    6. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2013. "Limit order books," Quantitative Finance, Taylor & Francis Journals, vol. 13(11), pages 1709-1742, November.

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