基于复杂网络的金融风险和波
动传导行为分析
THE ANALYSIS OF THE BEHAVIOR BASED ON THE FINANCIAL RISK OF COMPLEX NEWORKS AND VOLATILITITY CONDUCTION
专 业：2010信息与计算科学 指 导 教 师：
申请学位级别： 学 士
论文提交日期：2014年6月8日
摘 要
20 世纪90年代以来，随着计算机科学、图论理论科学的不断探索，复杂网络学科慢慢走入人们的视线并且快速发展起来。目前，金融经济领域的复杂网络理论的研究也日益增多。本文便是基于复杂网络中无尺度模型的统计特征对股票市场进行波动分析的。
此外，已知股票市场上不同股票的收益相互之间会存在影响，由此可看出股票间相关系数矩阵及对应距离矩阵可用来对股票相互作用关系进行分析。在此基础上提取的最小生成树网络常见用来研究股票结构。
本文首先选取了2012年1月4日至14年5月5日中上证50指数中股票的日收盘价,以股票为节点,以股票收益率相关系数的度量距离为边构建复杂网络，利用prim算法将股票收益率相关系数反映到最小生成树网络即所求的最小生成树。然后对该网络进行分析并由此得出该网络的统计特性，即统计股票价格收益和价格波动网络中中心节点的数目，计算网络度分布、平均度和平均路径，也就是无尺度网络的特性，然后在此基础上分析了各股票收益率波动之间的联系。
通过分析我们可以看到在上证50指数成份股中，存在几只特定股票包含较高的度，他们的收益率变动会对其他股票的波动产生较为明显的影响。而总体上各支股票度的大小差距不明显也可以看出这些股票中缺乏影响力
很强的股票，这也是我国股票于外国股市最大的区别之一。
关键词：最小生成树； 无尺度网络； 股票网络； 收益率波动
ABSTRACT
Since the 1990s, with the continuous exploration of the computer science and the graph theory science, the complex network disciplines gradually into people’s sight and quickly developed. Currently, the study of complex networks theory in the field of financial economics is increasing day by day. This article is run the analysis of the fluctuation of stock market based on the statistical characteristics of scale-free complex network model.
Furthermore, it’s known that the interactions of the benefits between the different stocks of stock market, which can be seen the correlation matrix between the stock and the corresponding correlation matrix distance matrix can be used to analyze the interaction between the stock. On this basis, the minimum spanning tree network extraction common stock used to study the structure. The minimum spanning tree network extraction on this basis common used to study the structure of stock. Firstly, we select the closing price of stocks of SSE 50 index between the January 04 of 2012 to May 05 of 2014,the node is made by the stocks, the edge of the complex networks is build by measure the distance of the stock returns. The minimum spanning tree requested is reflecting by using prim algorithm put the correlation coefficient of stock yields into minimum spanning tree network. Then draw statistical properties of the network by the analyze of this network, it’s also the number of the central node of the network of statistics that stock price gains and price volatility, next, computing network distribution, the average degree and average path,
which is characteristic of scale-free networks, and then analysis of the links between the various fluctuations in stock returns on the basis of the network.
We can see there are a few specific stocks contains a the SSE 50 Index constituent stocks through analysis, their yield changes will produce more significant impact within other stocks fluctuate. Over all, the lack of influence strong stocks of these stocks can be seen by the size of the various stocks is obvious disparity, which is also the biggest difference between the stocks of our country and foreign stocks.
Key words： Minimum spanning tree; scale-free networks; the stock
of network; yield fluctuation
目 录
1 绪论 ................................................. 1 1.1 课题研究的背景与意义 ................................ 1 1.2 复杂网络研究现状及其理论综述 ........................ 1 1.3 本文主要研究内容 .................................... 4
2 最小生成树型复杂网络概述 ............................. 5 2.1 最小生成树相关理论 .................................. 5 2.2 最小生成树常见算法 .................................. 6
2.3 本章小结 ........................................... 7
3 基于最小生成树的股票收益率网络建立与分析 .............. 8 3.4 股票相关知识 ........................................ 8 3.5 股票价格发生波动的原因分析 ......................... 10 3.6 基于最小生成树的股票收益率关联网络构建 ............. 14 3.7 对股票关联网络进行的总体分析 ....................... 22 3.8 对股票关联网络波动及风险防范分析 ................... 24 3.9 本章小结 .......................................... 27
4 结论 ................................................ 28
参考文献 ............................................... 30
致 谢 ................................................. 31
附 录 ................................................. 32
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