用Langevin方法描述股票价格动态
Description of dynamics of stock prices by a Langevin approach
摘要：
我们提出了一个时间依赖的股票价格的动态朗之万描述。基于一个简单的滑动窗口算法，从一个依赖于时间的线性回复力的角度讨论了股票价格的波动，该恢复力是由金融时间序列估计的Langevin方程中漂移参数的线性近似.通过选择合适的加权因子进行线性逼近，推导出金融时间序列的自相关性与回复力的动态效应之间的关系。我们特别分析了S $&$ P500指数1950 - 1999年的日对数收益率。从回复力的斜率系数和均衡位置两个方面考察了恢复力对价格演变的意义。从统计和理论分析得到的新的简单形式的回复力表明，朗之万方法可以有效地反映价格演变的宏观和细节性质。
英文摘要：
We present a time-dependent Langevin description of dynamics of stock prices. Based on a simple sliding-window algorithm, the fluctuation of stock prices is discussed in the view of a time-dependent linear restoring force which is the linear approximation of the drift parameter in Langevin equation estimated from the financial time series. By choosing suitable weighted factor for the linear approximation, the relation between the dynamical effect of restoring force and the autocorrelation of the financial time series is deduced. We especially analyze the daily log-returns of S$&$P 500 index from 1950 to 1999. The significance of the restoring force towards the prices evolution are investigated from its two coefficients, slope coefficient and equilibrium position. The new simple form of the restoring force obtained both from statistical and theoretical analyses suggests that the Langevin approach can effectively present the macroscopical and the detail properties of the price evolution.
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