基于复杂网络的金融市场建模方法研究

发布时间：2018-05-03 06:27

本文选题：复杂系统 + 复杂网络　；参考：《中国科学技术大学》2013年博士论文

【摘要】：近年来,通过对金融市场历史数据的统计分析,发现得到的结论与传统金融市场的三大理论：理性经理人、随机漫步模型和有效市场假说存在不小的偏差。人们需要新的非线性方法来研究金融市场,以找到真实市场的演化机制,弥补传统金融理论对真实市场众多现象不能解释的缺陷。20世纪80年代发展出来的复杂性科学在处理非线性问题上的成功,为金融理论的进一步发展创造了机会。伴随着金融理论的发展,金融市场建模日渐盛行其中,出现了如元胞自动机,伊辛,GARCH等模型。这些模型对金融市场的某些特征进行了比较好的模拟,但都有各自不足。因此建立更好更全面的模型就是本文工作的重点。本文对金融市场进行建模研究,基于无标度网络的逾渗理论和动态异质投资群体结构,通过多个智能体在交易规则约束下的聚簇行为,建立金融市场的自组织演化市场模型,并将该模型与真实市场进行对比,主要研究了市场的价格的波动特征及整个市场的动态演化机制。其次基于股票价格波动序列的相关特性,通过阈值化处理,建立加权网络金融市场模型,通过对模型分析获得了金融网络的层次性、匹配性及最深核等特性。本文的主要工作和创新如下： (1)针对随机游走模型和对数周期性幂率模型等传统宏观金融模型不能解释金融市场程式化特征的问题,提出一个微观的能产生符合真实金融市场程式化特征的模型；模型产生的价格时间序列能对多种程式化特性进行模拟,如价格波动的相关性、价格收益的聚集性、收益分布的尖峰胖尾特性等等,表明该模型能够再现真实市场,模拟市场价格波动行为,同时找到了真实市场中存在的但传统金融理论却不能解释的现象的产生机制,即羊群效应和市场网络拓扑结构的自组织非线性演化。 (2)针对原始CB模型及其改进模型中投资群体个体间不具备差异性的缺点,提出一种基于复杂网络逾渗理论的金融市场模型,解决了投资群体结构的动态异质性问题,模型中交易者之间的连接关系构成了一个无标度网络,使得参与交易的个体具有不同的地位,并且投资个体随时加入、离开网络,网络的拓扑结构随时发生变化。 (3)针对股票间交互关系程度不能直观判定的问题,提出基于相关性的加权金融网络模型,解决了多支股票交互关系的量化问题。 (4)针对不同阈值的加权金融网络,采用复杂网络方法进行定量分析,计算网络的平均度、聚类系数、最近邻和核结构等系数,发现金融市场中少数节点具有更大的影响力并且具有层次性、异配性和富人俱乐部等性质,这些性质与实际观察一一吻合。这些研究成果表明,本文所建立的金融市场模型可以对现实金融市场价格时间序列的多数特性进行相对精确的模拟,有助于理解金融系统的内在运行机制,并为建立金融市场预测模型提供一定的依据和借鉴。
[Abstract]:In recent years, through the statistical analysis of the historical data of the financial market, it is found that there are no small deviations between the conclusions and the three theories of the traditional financial market: rational managers, random walk model and effective market hypothesis. People need new nonlinear methods to study the financial market, in order to find the real market evolution mechanism and make up for the transmission. The failure to explain the many phenomena of real market by the theory of unified finance, the success of the complexity science developed in the 80s of the.20 century in dealing with the nonlinear problems has created an opportunity for the further development of the financial theory.
With the development of financial theory, the modeling of financial market is becoming more and more popular, such as cellular automata, isin, GARCH and other models. These models have been well simulated on some characteristics of the financial market, but they have their own shortcomings. Therefore, the focus of this work is to establish a better and more comprehensive model.
Based on the percolation theory of scale-free networks and the structure of dynamic heterogeneous investment group, this paper builds a self organizing evolution market model of financial markets based on the percolation theory of scale-free networks and the structure of dynamic heterogeneous investment group, and compares the model to the real market. Dynamic characteristics and the dynamic evolution mechanism of the whole market. Secondly, based on the related characteristics of the stock price fluctuation sequence, the weighted network financial market model is established by threshold processing, and the characteristics of the hierarchy, matching and the deepest core of the financial network are obtained through the analysis of the model.
The main work and innovation of this article are as follows:
(1) in view of the problem that the traditional macro financial models, such as random walk model and logarithmic periodic power rate model, can not explain the stylized characteristics of financial markets, a micro model which can produce the stylized characteristics of the real financial market is proposed. The price time series generated by the model can simulate various stylized characteristics, such as price wave. The dynamic correlation, the aggregation of price income, the peak and fat tail of the income distribution, and so on, show that the model can reproduce the real market, simulate the market price fluctuation, and find the mechanism of the phenomenon that the real market exists but the traditional financial theory can not explain, that is the herd effect and the market network topology. Nonlinear evolution of self - organization.
(2) a financial market model based on complex network percolation theory is proposed to solve the problem of dynamic heterogeneity in the structure of investment group. The connection between traders in the model constitutes a scale-free network in the model, which makes the participation of the transaction in the original CB model and its improved model. The individual has different status, and the investment individual will join in and leave the network at any time. The topological structure of the network will change at any time.
(3) a weighted financial network model based on correlation is proposed to solve the problem of quantifying the interaction of multiple stocks in order to solve the problem that the degree of mutual relations between stocks can not be judged directly.
(4) according to the weighted financial networks with different thresholds, the complex network method is used to carry out quantitative analysis. The average degree of the network, the clustering coefficient, the nearest neighbor and the kernel structure are calculated. It is found that a few nodes in the financial market have greater influence and have the properties of hierarchical, unmatched and rich clubs. These properties and actual observation are observed. One by one.
These results show that the financial market model established in this paper can accurately simulate most of the characteristics of the real financial market price time series, and help to understand the internal operating mechanism of the financial system, and provide a certain basis and reference for the establishment of the model of the financial market prediction.

【学位授予单位】：中国科学技术大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F830.91;F224

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