Description of dynamics of stock prices by a Langevin approach  

作　　者：黄子罡 陈勇 张勇 汪映海 

机构地区：[1]Institute of Theoretical Physics, Lanzhou University, Lanzhou 730000, China [2]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

出　　处：《Chinese Physics B》2007年第4期975-983,共9页中国物理B（英文版）

基　　金：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）. We would like to thank Professor Zhao Hong and Dr Xu Xin-Jian for helpful discussions.

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.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 

分 类 号：F830.91[经济管理—金融学]