Description of dynamics of stock prices by a Langevin approach

• 来源期刊: 中国物理（英文版）
• 关键词: financial time series Langevin approach drift parameter autocorrelation
• 年，卷（期）: 2007,（4）
• 页码范围: 975-983
• 页数: 9页
• 语种: 英文

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.