基于行为金融实验的非线性证券价格动态模型

Nonlinear Dynamic Model of Security Price Based on Behavioral Finance Experiments

为了研究交易者资产结构与股价波动之间的关系,设计并实施了10场内容相同的行为金融实验。根据实验现象以及交易者持仓状态反映其对市场的投资态度,构建了描述市场平均投资态度和股票价格的数学模型。首先利用离散动力系统的相关理论研究了模型的稳定性,然后根据金融市场稳定与否对传染效应进行界定。数值模拟发现,在理性传染效应区间内,存在最优传染效应。在此基础上,进一步探讨了资产结构与股价波动之间的关系。具体而言,在理性传染效应的作用下,当市场中满仓交易者数量与空仓交易者数量相当时,股价呈现小幅水平趋势波动;当满仓交易者数量远高于(低于)空仓交易者数量,股价呈现大幅下跌(上涨)趋势波动。

To explore the relationship between traders capital structure and stock price volatility, we design and implement ten behavioral finance experiments with the same contents. According to the experimental phenomena and the principle that the positions of traders reflect their investment attitude towards market, this paper constructs a mathematical model describing the average market investment attitude and stock price. We first study the stability of the model by the related theory of nonlinear discrete dynamic system, and then identify contagion effect based on whether financial market is stable. Numerical simulations indicate that there exists an optimal contagion effect in the region of ra- tional contagion effect. Furthermore, it also investigates the relationship between capital structure and stock price volatility when contagion effect is rational. Specifically, under the influence of rational contagion effect, when the numbers of long position traders and short position traders are roughly equal in the market, share price volatility shows a parallel trend with slight amplitude when the number of long position traders are more （less） than the number of short position traders, share price volatility shows a decline （an upward） trend in huge amplitude.