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The oscillation of stock price by majority orienting traders with investment position

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  • Yamashita, T.
  • Itoh, Y.

Abstract

We consider an interacting particle system for the stock price fluctuation. The change of the stock price with a feedback by the price considering the herding behavior (majority orienting behavior) of traders, gives the van der Pol equation as a deterministic approximation. Considering the investment position of each trader, we introduce the delayed van der Pol equation. The history of investment positions, for example sell or buy, of each trader for a stock makes a memory effect, which is modeled by using the time retardation. The delayed van der Pol equation model seems to be natural and explains typical phenomena, for example triangle pattern, volatility jumps, price jumps and price trends, known for the time series of a stock price.

Suggested Citation

  • Yamashita, T. & Itoh, Y., 2007. "The oscillation of stock price by majority orienting traders with investment position," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 374(2), pages 764-772.
    • Handle: RePEc:eee:phsmap:v:374:y:2007:i:2:p:764-772
    DOI: 10.1016/j.physa.2006.08.021
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    References listed on IDEAS

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    1. H. Takahashi & Y. Itoh, 2004. "Majority orienting model for the oscillation of market price," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 37(2), pages 271-274, January.
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    3. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    4. Bjørn Eraker, 2004. "Do Stock Prices and Volatility Jump? Reconciling Evidence from Spot and Option Prices," Journal of Finance, American Finance Association, vol. 59(3), pages 1367-1404, June.
    5. Shiller, Robert J., 1999. "Human behavior and the efficiency of the financial system," Handbook of Macroeconomics, in: J. B. Taylor & M. Woodford (ed.), Handbook of Macroeconomics, edition 1, volume 1, chapter 20, pages 1305-1340, Elsevier.
    6. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    7. Hisanao Takahashi & Yoshiaki Itoh, 2004. "Majority Orienting Model for the Oscillation of Market Price," Papers nlin/0403056, arXiv.org.
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    Cited by:

    1. Ueda, Sumie & Makino, Kumi & Itoh, Yoshiaki & Tsuchiya, Takashi, 2015. "Logistic growth for the Nuzi cuneiform tablets: Analyzing family networks in ancient Mesopotamia," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 223-232.

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