反馈交易与证券市场收益的尖峰厚尾特征

Feedback Trading and Fat-tail Distribution of Stock Market Returns

提出了一个有理性交易者和非理性交易者参与的证券市场收益模型,其中非理性交易者采取简单趋势外推的反馈交易策略。反馈交易导致收益序列的自相关,收益序列的长程相关性引起了异常扩散,由于扩散的方差大于标准布朗运动的方差,造成收益概率密度函数的厚尾现象。在模型的基础上,利用蒙特卡罗仿真方法生成了股市收益时间序列样本,计算了仿真数据的峰度、尾指数和自相关系数,并与我国上证指数真实收益序列的相应指标进行了对比分析。模型的仿真结果显示了证券收益的尖峰厚尾特征以及收益序列的自相关性。

This paper establishes a model of stock market returns which involves the participation of rational traders and irrational traders, who adopt feedback trading strategy. The long-term autocorrelation of return series caused by feedback trading strategy results in anomalous diffusion, thus leading to fat tail phenomenon of the probability density function of the stock returns. Based on the model, we use Monte Carlo simulation method to produce a time series, compute the kurtosis, tail-index and the autocorrelation coefficient of the time series and compare it with the corresponding index of the real return series of Shanghai stock markets. It turns out that this model can sufficiently illustrate the characteristics of fat-tail and autocorrelation of stock market returns.