中国物理B ›› 2007, Vol. 16 ›› Issue (4): 975-983.doi: 10.1088/1009-1963/16/4/019

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Description of dynamics of stock prices by a Langevin approach

张勇1, 黄子罡2, 陈勇2, 汪映海2   

  1. (1)Department of Physics, Center for Nonlinear Studies, and The Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, Hong Kong, China; (2)Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:2006-07-27 修回日期:2006-08-16 出版日期:2007-04-20 发布日期:2007-04-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 10305005), the Fundamental Research Fund for Physics and Mathematics of Lanzhou University (Grant No Lzu05008).

Description of dynamics of stock prices by a Langevin approach

Huang Zi-Gang(黄子罡)a), Chen Yong(陈勇)a), Zhang Yong(张勇)b), and Wang Ying-Hai(汪映海)a)   

  1. a Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China; b Department of Physics, Center for Nonlinear Studies, and The Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems (Hong Kong), Hong Kong Baptist University, Kowloon Tong, Hong Kong, China
  • Received:2006-07-27 Revised:2006-08-16 Online:2007-04-20 Published:2007-04-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 10305005), the Fundamental Research Fund for Physics and Mathematics of Lanzhou University (Grant No Lzu05008).

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摘要： We have studied the Langevin description of stochastic dynamics of financial time series. A sliding-window algorithm is used for our analysis. We find that the fluctuation of stock prices can be understood from the view of a time-dependent drift force corresponding to the drift parameter in Langevin equation. It is revealed that the statistical results of the drift force estimated from financial time series can be approximately considered as a linear restoring force. We investigate the significance of this linear restoring force to the prices evolution from its two coefficients, the equilibrium position and the slope coefficient. The daily log-returns of S&P 500 index from 1950 to 1999 are especially analysed. The new simple form of the restoring force obtained both from mathematical and numerical analyses suggests that the Langevin approach can effectively present not only the macroscopical but also the detailed properties of the price evolution.

关键词: financial time series, Langevin approach, drift parameter, autocorrelation

Abstract: We have studied the Langevin description of stochastic dynamics of financial time series. A sliding-window algorithm is used for our analysis. We find that the fluctuation of stock prices can be understood from the view of a time-dependent drift force corresponding to the drift parameter in Langevin equation. It is revealed that the statistical results of the drift force estimated from financial time series can be approximately considered as a linear restoring force. We investigate the significance of this linear restoring force to the prices evolution from its two coefficients, the equilibrium position and the slope coefficient. The daily log-returns of S&P 500 index from 1950 to 1999 are especially analysed. The new simple form of the restoring force obtained both from mathematical and numerical analyses suggests that the Langevin approach can effectively present not only the macroscopical but also the detailed properties of the price evolution.

Key words: financial time series, Langevin approach, drift parameter, autocorrelation

中图分类号:  (Stochastic analysis methods)

  • 05.10.Gg
05.45.Tp (Time series analysis) 89.65.Gh (Economics; econophysics, financial markets, business and management) 05.40.Ca (Noise) 02.50.Fz (Stochastic analysis)