Qiu G, Kandhai D, Sloot P M A
Section Computational Science, Faculty of Science, University of Amsterdam, Kruislaan 403, 1098 SJ Amsterdam, The Netherlands.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Apr;75(4 Pt 2):046116. doi: 10.1103/PhysRevE.75.046116. Epub 2007 Apr 26.
We present a cellular automaton (CA) model for simulating the complex dynamics of stock markets. Within this model, a stock market is represented by a two-dimensional lattice, of which each vertex stands for a trader. According to typical trading behavior in real stock markets, agents of only two types are adopted: fundamentalists and imitators. Our CA model is based on local interactions, adopting simple rules for representing the behavior of traders and a simple rule for price updating. This model can reproduce, in a simple and robust manner, the main characteristics observed in empirical financial time series. Heavy-tailed return distributions due to large price variations can be generated through the imitating behavior of agents. In contrast to other microscopic simulation (MS) models, our results suggest that it is not necessary to assume a certain network topology in which agents group together, e.g., a random graph or a percolation network. That is, long-range interactions can emerge from local interactions. Volatility clustering, which also leads to heavy tails, seems to be related to the combined effect of a fast and a slow process: the evolution of the influence of news and the evolution of agents' activity, respectively. In a general sense, these causes of heavy tails and volatility clustering appear to be common among some notable MS models that can confirm the main characteristics of financial markets.
我们提出了一种元胞自动机（CA）模型来模拟股票市场的复杂动态。在这个模型中，股票市场由一个二维晶格表示，其中每个顶点代表一个交易者。根据实际股票市场中的典型交易行为，只采用两种类型的主体：基本面分析者和模仿者。我们的CA模型基于局部相互作用，采用简单规则来表示交易者的行为以及价格更新的简单规则。该模型能够以简单且稳健的方式重现实证金融时间序列中观察到的主要特征。由于价格大幅波动而产生的重尾收益分布可以通过主体的模仿行为生成。与其他微观模拟（MS）模型不同，我们的结果表明，没有必要假设主体聚集在一起的特定网络拓扑结构，例如随机图或渗流网络。也就是说，长程相互作用可以从局部相互作用中产生。同样会导致重尾的波动聚集似乎与一个快速过程和一个缓慢过程的综合效应有关：分别是新闻影响力的演变和主体活动的演变。一般来说，这些导致重尾和波动聚集的原因在一些能够证实金融市场主要特征的著名MS模型中似乎是常见的。
