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Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis

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  • Xiao, Di
  • Wang, Jun

Abstract

The continuum percolation system is developed to model a random stock price process in this work. Recent empirical research has demonstrated various statistical features of stock price changes, the financial model aiming at understanding price fluctuations needs to define a mechanism for the formation of the price, in an attempt to reproduce and explain this set of empirical facts. The continuum percolation model is usually referred to as a random coverage process or a Boolean model, the local interaction or influence among traders is constructed by the continuum percolation, and a cluster of continuum percolation is applied to define the cluster of traders sharing the same opinion about the market. We investigate and analyze the statistical behaviors of normalized returns of the price model by some analysis methods, including power-law tail distribution analysis, chaotic behavior analysis and Zipf analysis. Moreover, we consider the daily returns of Shanghai Stock Exchange Composite Index from January 1997 to July 2011, and the comparisons of return behaviors between the actual data and the simulation data are exhibited.

Suggested Citation

  • Xiao, Di & Wang, Jun, 2012. "Modeling stock price dynamics by continuum percolation system and relevant complex systems analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4827-4838.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:20:p:4827-4838
    DOI: 10.1016/j.physa.2012.05.024
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    2. Zeng, Yayun & Wang, Jun & Xu, Kaixuan, 2017. "Complexity and multifractal behaviors of multiscale-continuum percolation financial system for Chinese stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 364-376.
    3. Jia, Linlu & Ke, Jinchuan & Wang, Jun, 2019. "Volatility aggregation intensity energy futures series on stochastic finite-range exclusion dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 370-383.
    4. 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.
    5. Zhang, Bo & Wang, Guochao & Wang, Yiduan & Zhang, Wei & Wang, Jun, 2019. "Multiscale statistical behaviors for Ising financial dynamics with continuum percolation jump," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1012-1025.
    6. Xiao, Di & Wang, Jun, 2021. "Attitude interaction for financial price behaviours by contact system with small-world network topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 572(C).
    7. Di Xiao & Jun Wang & Hongli Niu, 2016. "Volatility Analysis of Financial Agent-Based Market Dynamics from Stochastic Contact System," Computational Economics, Springer;Society for Computational Economics, vol. 48(4), pages 607-625, December.
    8. Wang, Jie & Wang, Jun, 2016. "Forecasting energy market indices with recurrent neural networks: Case study of crude oil price fluctuations," Energy, Elsevier, vol. 102(C), pages 365-374.
    9. Ko, Bonggyun & Kim, Kyungwon, 2017. "Simulation of sovereign CDS market based on interaction between market participant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 479(C), pages 324-340.
    10. Niu, Hongli & Wang, Jun & Lu, Yunfan, 2016. "Fluctuation behaviors of financial return volatility duration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 30-40.
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    12. Hongli Niu & Jun Wang, 2014. "Phase and multifractality analyses of random price time series by finite-range interacting biased voter system," Computational Statistics, Springer, vol. 29(5), pages 1045-1063, October.

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