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Finite-Range Contact Process On The Market Return Intervals Distributions

Author

Listed:
  • JUNHUAN ZHANG

    (Institute of Financial Mathematics and Financial Engineering, College of Science, Beijing Jiaotong University, Beijing 100044, China)

  • JUN WANG

    (Institute of Financial Mathematics and Financial Engineering, College of Science, Beijing Jiaotong University, Beijing 100044, China)

  • JIGUANG SHAO

    (Institute of Financial Mathematics and Financial Engineering, College of Science, Beijing Jiaotong University, Beijing 100044, China)

Abstract

Stochastic system is applied to describe and investigate the fluctuations of stock price changes in a stock market, and a stock price model is developed by the finite-range contact process of the statistical physics systems. In this paper, the scaling behaviors of the return intervals for SSE Composite Index (SSE) and the simulation data of the model are investigated and compared. The database is from the index of SSE in the 6-year period for every 5 minutes, and the simulation data is from the finite-range contact model for different values of the rangeR. For different values of threshold θ, the statistical analysis shows that the probability density functionPθ(τ)of the return intervals τ for both SSE and the simulation data have similar scaling form, that is$P_{\theta}(\tau) = {\bar{\tau}}^{-1}h(\tau\/\bar{\tau})$($\bar{\tau}$is the mean return interval), where the scaling functionh(x)can be approximately fitted by the functionh(x) = ωe-a(ln x)γ, and ω,a, γ are three parameters. Further, with different values ofRand θ, the statistical comparison of SSE Composite Index and simulation data are given.

Suggested Citation

  • Junhuan Zhang & Jun Wang & Jiguang Shao, 2010. "Finite-Range Contact Process On The Market Return Intervals Distributions," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 13(05), pages 643-657.
    • Handle: RePEc:wsi:acsxxx:v:13:y:2010:i:05:n:s0219525910002797
    DOI: 10.1142/S0219525910002797
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    References listed on IDEAS

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    1. Kirill Ilinski, 1997. "Physics of Finance," Papers hep-th/9710148, arXiv.org.
    2. Antonio Caparrós Ruiz & Mª. Lucía Navarro Gómez, 2002. "Factors affecting quits and layoffs in Spain," Economic Working Papers at Centro de Estudios Andaluces E2002/16, Centro de Estudios Andaluces.
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    Cited by:

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    2. Niu, Hongli & Wang, Jun, 2013. "Complex dynamic behaviors of oriented percolation-based financial time series and Hang Seng index," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 36-44.
    3. Wang, Guochao & Zheng, Shenzhou & Wang, Jun, 2020. "Fluctuation and volatility dynamics of stochastic interacting energy futures price model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Gu, Danlei & Huang, Jingjing, 2019. "Multifractal detrended fluctuation analysis on high-frequency SZSE in Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 225-235.
    5. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    6. Zhang, Bo & Wang, Jun & Fang, Wen, 2015. "Volatility behavior of visibility graph EMD financial time series from Ising interacting system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 432(C), pages 301-314.
    7. Junhuan Zhang & Peter McBurney & Katarzyna Musial, 2018. "Convergence of trading strategies in continuous double auction markets with boundedly-rational networked traders," Review of Quantitative Finance and Accounting, Springer, vol. 50(1), pages 301-352, January.

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