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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, September.
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    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. Lux, Thomas, 2008. "Applications of statistical physics in finance and economics," Kiel Working Papers 1425, Kiel Institute for the World Economy (IfW Kiel).
    4. Kyrylo Shmatov & Mikhail Smirnov, 2005. "On Some Processes and Distributions in a Collective Model of Investors' Behavior," Papers nlin/0506015, arXiv.org.
    5. 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.
    6. 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.

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