复杂金融网络若干问题研究

发布时间：2018-02-27 14:53

本文关键词： 复杂性金融网络金融物理相关系数　出处：《华东理工大学》2013年博士论文　论文类型：学位论文

【摘要】：金融市场是一个受到大量不同对象相互作用和相互影响,从而表现出各种复杂多变现象的复杂系统。伴随着金融物理学等新兴交叉性学科的出现,数学、统计物理、几何学等方法和思想被运用到金融市场中。本文从两类复杂网络入手,进而将重心转向时间序列相关性,对不同规模、不同对象的金融市场分别进行分析和探讨。首先,我们研究了全世界上百个经济体的相互投资行为,以2001年到2006年的投资行为为样本,构造了30个复杂网络。通过分析世界投资网络的统计性质,发现世界的投资行为正在日益全球化。另外,我们也发现世界投资网络是无标度的,并具有小世界的特性。世界投资网络的边权重服从Weibull分布,节点强度服从幂律分布。世界投资网络也表现出了一定的富人俱乐部特性以及异配性。异速生长标度指数是η=1.17±0.02,异速生长流标度指数是ζ=1.03±0.01。其次,我们以世界57个国家和地区的股票指数的日度收益率为研究对象,用日度收益率时间序列的相关系数来构建复杂网络,通过计算复杂网络的最大平面图以及最大平面图的社团结构,我们发现这些指数能够按照地域性被较好划分开来。复杂网络边权重的均值的快速动态演化较好的对应一些历史上的重要金融危机。我们证明3个月长度的时间窗口能较好的用于研究,最大平面图的互信息变换、最大平面图的节点度数以及相关系数矩阵的第一、第二特征值和第一、第二特征向量都显示出相应的信息。我们将相关系数转变成对应节点之间的距离之后,通过距离构建最小生成树,并分析最小生成树的标准化树长、单步保有率和异速生长,发现在那些金融危机的时间点,最小生成树的标准化树长发生较大的变化,同时边发生了大量的替换,而在传输效率方面,结构变得更加高效。接着,我们针对上海证券交易所的255只股票进行相关系数和偏相关系数的分析和对比。收益率在相关系数和偏相关系数的第一特征向量上投影的和上证指数的收益率具有很好的线性关系。我们分离相关系数矩阵和偏相关系数矩阵,并对分离出来的对象进行Block的分块研究,并且发现偏相关系数能比相关系数更好的进行分块。然后,我们引入了Hayashi和Y'oshida提出的异步相关系数算法。对于欧洲6个证券交易所的活跃股票,分别计算不同时间间隔的皮尔逊相关系数以及异步相关系数。发现1分钟时间间隔的时间相关系数对于异步相关系数有一个“向下”的偏移现象。在通过对比基于皮尔逊相关系数的最小生成树和用异步相关系数修正过的最小生成树,发现在阿姆斯特丹、伦敦、布鲁塞尔和马德里这4个证券交易所的股票之间存在较多的由于皮尔逊相关系数的“向下”偏移而导致的结构变化,同时发现这四个证券交易所中股票的连续买卖交易之间间隔的平均时间都近似或者大于1分钟。这些最小生成树和基于异步相关系数的最小生成树都以各自的证券交易所而聚成一类,而不同的证券交易所之间也会以相同的行业进行相连。最后,我们使用之前引入的异步相关系数对宝钢股份和宝钢JTB1的持仓变化量进行分析。相关系数的分布都在一定范围内服从指数分布,而在0的附近则主要服从幂律分布。分析宝钢JTB1的异步相关系数矩阵的特征值和特征向量,发现持仓变化量在异步相关系数的第一特征向量上的投影,随着时间一分为二,收益率与持仓变化量投影之间在前后两端有着不同的线性关系,前后斜率相差将近3倍。第二特征向量分量为负时,在我们定义的收益率之下,对应投资者的收益率多数为正,为正时则相反,在靠近0处,收益率正负性则不是很清晰。随着第二特征向量分量从小到大,投资者1分钟后的盈利情况成上升趋势。另外,投资者以短期投资为主要获利手段,而在这些短期投资中,主动成交要比被动成交更能获得收益。
[Abstract]:The financial market is a complex system which is influenced by a lot of different objects , thus exhibiting various complex and changeable phenomena . With the emergence of emerging cross disciplines such as finance physics , the methods and ideas of mathematics , statistical physics and geometry are applied to financial markets . This paper starts with two types of complex networks , and further analyzes and discusses the financial markets of different scales and objects . First , we have studied the mutual investment behavior of hundreds of economies around the world . By analyzing the statistical nature of the world ' s investment network , we have found that the world ' s investment behavior is increasingly globalized . In addition , we find that the world investment network is not scale and has the characteristics of small world . Secondly , based on the daily return of stock index of 57 countries and regions of the world , we construct a complex network by using the correlation coefficient of daily return time series . We find that these indexes can be divided better according to the regional characteristics . We prove that the time windows of 3 months length can be better used in the research , the maximum plan view mutual information transformation , the node degree of the maximum plan view and the first and second characteristic vectors of the correlation coefficient matrix show the corresponding information . We find that the minimum spanning tree has a great change in the time point of the financial crisis , and the structure becomes more efficient in terms of transmission efficiency . Secondly , we analyze and compare the correlation coefficient and the partial correlation coefficient of 255 stocks in Shanghai Stock Exchange . The yield has a good linear relationship with the yield of Shanghai Stock Exchange on the first feature vector of correlation coefficient and partial correlation coefficient . We separate the correlation coefficient matrix and the partial correlation coefficient matrix , and block the isolated objects , and find that the partial correlation coefficient can be better than the correlation coefficient . We have introduced Hayashi and Y ' oshida ' s asynchronous correlation coefficient algorithm . For the active stocks of six European stock exchanges , Pearson correlation coefficient and asynchronous correlation coefficient of different time intervals are calculated . In the end , we analyze the change of positions of Baosteel ' s shares and Baosteel ' s JTBs by using the asynchronous correlation coefficient introduced before we use them . The distributions of correlation coefficient are subject to exponential distribution within a certain range , while at 0 it is mainly subject to power law distribution . When the component of the second feature vector is negative , the profit of the corresponding investor is upward trend with the second characteristic vector component from small to large . In addition , the investor takes short - term investment as the main profit means , and in these short - term investments , the active transaction is more profitable than the passive transaction .

【学位授予单位】：华东理工大学
【学位级别】：博士
【学位授予年份】：2013
【分类号】：F830.9;O157.5

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