基于Ising模型的股票价格统计特征及模拟

Statistical Properties of Stock Price and Simulation by Ising Model

根据统计物理中的Ising模型和极限理论,研究证券市场中股票价格的统计规律.通过建立相应的金融收益模型,构造出股价的随机过程.再利用计算机模拟股票价格收益率的分布特征,模型很好的刻画了现实证券市场中股票收益率分布的宽尾现象、长记忆性,以及累积分布中尾部收益的指数递减现象.

We investigate the fluctuation of price process in a stock market with Ising model and the mean field theory, and construct the corresponding random logarithmic price returns process. According to the mean-field simulations of the model, the time series of logarithmic price returns exhibit bursting typical of volatility clustering. Distributions of price returns show the power-law tails, and the corresponding cumulative distributions have regions of power scaling, with exponents comparable to those observed in empirical time series of stock price returns.