Skip to main content
SpringerLink
Log in

A continuum percolation model for stock price fluctuation as a Lévy process

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

This paper concerns with two reasons for stock price fluctuation, the instinctive stochastic fluctuation and the fluctuation caused by the spread of information. They are constructed by compound Poisson process and continuum percolation model separately. Combining the two models, the authors get a Lévy process for the price fluctuation that can explain the fat-tail phenomenon in stock market. The fat-tails are also presented in numerical simulations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Fama E F, The behavior of stock market prices, Journal of Business, 1965, 38: 34–105.

    Article  Google Scholar 

  2. Fama E F, Multiperiod consumption-investment decisions, American Economic Review, 1970, 60: 163–174.

    Google Scholar 

  3. Godfrey M, Granger C, and Morgenstern O, The random-walk hypothesis of stock market behavior, Kyklos, 1964, 17: 1–30.

    Article  Google Scholar 

  4. Fama E F, Random walks in stock market prices, Financial Analyst Journal, 1965, 21(5): 55–59.

    Article  Google Scholar 

  5. Black F and Scholes M, The pricing of options and corporate liabilities, Journal of Political Economy, 1973, 81: 637–654.

    Article  Google Scholar 

  6. Lo A and MacKinlay A, Stock market prices do not follow random walks: Evidence from a simple specification test, Review of Financial Studies, 1988, 1(1): 41–66.

    Article  Google Scholar 

  7. Shiller R J, Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review, 1981, 71: 421–436.

    Google Scholar 

  8. Stauffer D and Penna T, Crossover in the cont-bounchaud percolation model for market fluctuations, Physica A, 1998, 256: 284–290.

    Article  Google Scholar 

  9. Stauffer D and Aharony A, Introduction to Percolation Theory, 2nd ed., Taylor & Francis, London, 1991.

    Google Scholar 

  10. Tanaka H, A percolation model of stock price fluctuations, Mathematical Economics (Japanese, Kyoto), 2002, 1264: 203–218.

    Google Scholar 

  11. Grimmett G, Percolation, 2nd ed., Springer-Verlag, New York, 1999.

    Book  MATH  Google Scholar 

  12. Wang N and Wang J, Construction and simulation of stock price fluctuation process by using Poisson boolean model, Journal of Beijing Jiaotong University, 2005, 29(3): 25–28.

    Google Scholar 

  13. Wang N, Wang J, and Dong G, Construction of stock index fluctuation model by continuum percolation and it’s discussion, Mathematica Applicata, 2009, 22(1): 65–71.

    MATH  MathSciNet  Google Scholar 

  14. Wang J, Wang Q, and Shao J, Fluctuations of stock price model by statistical physics systems, Mathematical and Computer Modelling, 2010, 51: 431–440.

    Article  MATH  MathSciNet  Google Scholar 

  15. Kyprianou A, Introductory Lectures on Fluctuations of Lévy Processes with Applications, Springer-Verlag, Berlin, 2006.

    MATH  Google Scholar 

  16. Applebaum D, Lévy Process and Stochastic Calculus, 2nd ed., Cambridge University Press, Cambridge, 2009.

    Book  Google Scholar 

  17. Cont R and Tankov P, Financial Modelling with Jump Process, Chapman and Hall, Londen, 2004.

    Google Scholar 

  18. Meester R and Roy R, Continuum Percolation, Cambridge University Press, Cambridge, 1996.

    Book  MATH  Google Scholar 

  19. Shao Y and Diao Y, Micro Finance with Its Mathematical Foundation, 2nd ed., Tsinghua Univiesity Press, Beijing, 2008.

    Google Scholar 

  20. Xiao D and Wang J, Modeling stock price dynamics by continuum percolation system and relecant complex systes analysis, Physica A, 2012, 319: 4827–4838.

    Article  Google Scholar 

  21. Mantegna R and Stanley H, An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press, Cambridge, 2000.

    Google Scholar 

  22. Cont R and Bounchaud J P, Herd behavior and aggregate fluctuations in fincncial market, Macroeconomic Dynamics, 2000, 4: 170–196.

    Article  MATH  Google Scholar 

  23. Gabaix X, Gopikrishnan P, Plerou V, and Stanley H, A theory of power-law distributions in financial market fluctuations, Nature, 2003, 423: 267–270.

    Article  Google Scholar 

  24. Wang J, Random walk on the poisson point of infinite cluster of the continuous percolation, Math. Japonica, 1998, 48(3): 391–397.

    MATH  Google Scholar 

  25. Wang J, Stochastic Process and Its Application in Finance, Tsinghua University Press and Beijing Jiaotong University Press, Beijing, 2007.

    Google Scholar 

  26. Wang Y, Qin Y, Niu H, and Wang J, Analysis and modelling of stock market relative fluctuation by percolation system, Journal of Information & Computational Science, 2012, 9(3): 771–779.

    Google Scholar 

  27. Stanley H, Andrade J, Havlin S, Makse S, and Suki H, Percolation phenomena: A broad-brush introduction with some recent applications to porous media, Liquid water and city growth, Physica A, 1999, 266: 5–16.

    Google Scholar 

  28. Stauffer D and Jan N, Sharp peaks in the percolation model for stock markets, Physica A, 2000, 277: 215–219.

    Article  Google Scholar 

  29. Stauffer D and Sornette D, Self-organized percolation model for stock market fluctuations, Physica A, 1999, 271: 496–506.

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. College of Management and Economics, Tianjin University, Tianjin, 300072, China

    Ning Wang & Ximin Rong

  2. Department of Science and Technology of Information, Tianjin University of Finance and Economics, Tianjin, 300222, China

    Ning Wang

  3. School of Science, Tianjin University, Tianjin, 300072, China

    Ximin Rong

  4. Center for Applied Mathematics of Tianjin University, Tianjin, 300072, China

    Ximin Rong

  5. Department of Mathematics, Tianjin Polytechnic University, Tianjin, 300160, China

    Guanghua Dong

Authors
  1. Ning Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ximin Rong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Guanghua Dong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ning Wang.

Additional information

This research was supported by the Natural Science Foundation of Tianjin, China under Grant No. 09JCYBLJC01800 and the China Postdoctoral Science Foundation Funded Project under Grant No. 20110491248.

This paper was recommended for publication by Editor ZOU Guohua.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Wang, N., Rong, X. & Dong, G. A continuum percolation model for stock price fluctuation as a Lévy process. J Syst Sci Complex 28, 175–189 (2015). https://doi.org/10.1007/s11424-014-2273-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-014-2273-z

Keywords

Search

Navigation