σ-熵曲线及其在金融市场中的应用
发布时间：2018-09-17 15:56
【摘要】：为了刻画边权网络的异质性，以及考察股票网络中的异质性与这些异质性的来源，基于股票的距离构建了股票网络，在网络结构熵的基础上给出了新概念σ-熵曲线与τ-值，，说明了定义的合理性以及不同的网络的异质性可以由τ-值的计算结果进行对比。越小于1的τ-值对应的网络的异质性越大，反之越接近1对应的网络的异质性越小。计算了具有市场代表性的沪深300指数与SP500指数的股票集合在不同年份的τ-值，同时为了对比行业与市场之间的差别，也计算了少数拥有较多公司的行业对应的网络的τ-值，比较了不同时间段不同行业与指数对应的τ-值的大小。另一方面，基于股票集合的相关系数矩阵计算了第一特征值与对应的第一主成分，验证了市场中存在少数经济因子。使用几何布朗运动构建了股票网络的模型，计算了对应的τ-值。最后针对σ-熵曲线与τ-值的概念以及性质进行了一些数值计算检验。 本文的计算结果表明，基于股票收盘价的网络对应的τ-值均小于1，呈现出一定的异质性，而单纯的几何布朗运动模拟出的网络的τ-值等于1，没有呈现出异质性。基于τ-值与相关的主成分以及随机矩阵理论的分析结果，对股票网络的异质性的来源进行了分析，股票网络存在异质性是因为市场中的元素对信息的反应具有异质性，股票网络的异质性体现了金融市场的复杂性的一个方面。
[Abstract]:In order to characterize the heterogeneity of the edge weight network and investigate the heterogeneity and the source of these heterogeneity in the stock network, the stock network is constructed based on the distance of the stock. Based on the entropy of the network structure, a new concept 蟽-entropy curve and 蟿-value are given. The rationality of the definition and the heterogeneity of different networks can be compared by the calculation results of 蟿-value. The larger the heterogeneity of the network corresponding to 蟿-value less than 1, the smaller the heterogeneity of the network that is close to the corresponding value of 1. In order to compare the difference between industry and market, the 蟿-value of the corresponding network of a few industries with more companies is also calculated in order to compare the 蟿-values of the stocks of CSI 300 index and SP500 index in different years, in order to compare the differences between industries and markets. The 蟿-values of different industries and indices in different time periods are compared. On the other hand, based on the correlation coefficient matrix of stock set, the first eigenvalue and the corresponding first principal component are calculated, which verifies the existence of a few economic factors in the market. The model of stock network is constructed by using geometric Brownian motion, and the corresponding 蟿-value is calculated. Finally, the concepts and properties of 蟽 -entropy curve and 蟿 -value are tested by numerical calculation. The calculated results show that the corresponding 蟿-values of the networks based on the closing price of stocks are less than 1, showing some heterogeneity, while the 蟿-values of the networks simulated by the simple geometric Brownian motion are equal to 1, and there is no heterogeneity. Based on the analysis results of 蟿 -value and related principal components and stochastic matrix theory, the source of heterogeneity of stock network is analyzed. The heterogeneity of stock network is due to the heterogeneity of elements in the market response to information. The heterogeneity of stock network reflects the complexity of financial market.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
本文编号：2246413
[Abstract]:In order to characterize the heterogeneity of the edge weight network and investigate the heterogeneity and the source of these heterogeneity in the stock network, the stock network is constructed based on the distance of the stock. Based on the entropy of the network structure, a new concept 蟽-entropy curve and 蟿-value are given. The rationality of the definition and the heterogeneity of different networks can be compared by the calculation results of 蟿-value. The larger the heterogeneity of the network corresponding to 蟿-value less than 1, the smaller the heterogeneity of the network that is close to the corresponding value of 1. In order to compare the difference between industry and market, the 蟿-value of the corresponding network of a few industries with more companies is also calculated in order to compare the 蟿-values of the stocks of CSI 300 index and SP500 index in different years, in order to compare the differences between industries and markets. The 蟿-values of different industries and indices in different time periods are compared. On the other hand, based on the correlation coefficient matrix of stock set, the first eigenvalue and the corresponding first principal component are calculated, which verifies the existence of a few economic factors in the market. The model of stock network is constructed by using geometric Brownian motion, and the corresponding 蟿-value is calculated. Finally, the concepts and properties of 蟽 -entropy curve and 蟿 -value are tested by numerical calculation. The calculated results show that the corresponding 蟿-values of the networks based on the closing price of stocks are less than 1, showing some heterogeneity, while the 蟿-values of the networks simulated by the simple geometric Brownian motion are equal to 1, and there is no heterogeneity. Based on the analysis results of 蟿 -value and related principal components and stochastic matrix theory, the source of heterogeneity of stock network is analyzed. The heterogeneity of stock network is due to the heterogeneity of elements in the market response to information. The heterogeneity of stock network reflects the complexity of financial market.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.9
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