关键词: 无标度网络, 逾渗理论, 金融市场, 自组织建模, Lévy分布

Abstract: For a series of grid-based Cont-Bouchaud (CB) models unable to correctly represent the heterogeneity of interactions among investors in the real financial market, an improved evolutionary model constrained by trading rules was proposed based on the percolation theory on scale-free networks. The time series of price fluctuations generated by the model was similar to the stock index in the real financial markets. For instances, the probability distributions of returns showed the sharp peak and fat tail, and their peak values restricted to the time scales obey the power-law behavior, which suggests that the time series of price fluctuations evolves in a self-similarity way. The clustering behavior of volatility shows that there are large fluctuations and long-range correlations in the evolutionary process. These statistical properties of return and volatility empirically are consistent with the real financial markets, indicating the effectiveness of the improved model.

Key words: scale-free network, percolation theory, financial market, self-organized model, Lévy distribution