Topological properties of stock market networks: The case of Brazil

This paper investigates the topological properties of the Brazilian stock market networks. We build the minimum spanning tree, which is based on the concept of ultrametricity, using the correlation matrix for a variety of stocks of different sectors. Our results suggest that stocks tend to cluster by sector. We employ a dynamic approach using complex network measures and find that the relative importance of different sectors within the network varies. The financial, energy and material sectors are the most important within the network.     

一种基于文本互信息的金融复杂网络模型

复杂网络能够解决许多金融问题,能够发现金融市场的拓扑结构特征,反映不同金融主体之间的相互依赖关系.相关性度量在金融复杂网络构建中至关重要.通过将多元金融时间序列符号化,借鉴文本特征提取以及信息论的方法,定义了一种基于文本互信息的相关系数.为检验方法的有效性,分别构建了基于不同相关系数(Pearson和文本互信息)和不同网络缩减方法(阈值和最小生成树)的4个金融复杂网络模型.在阈值网络中提出了使用分位数来确定阈值的方法,将相关系数6等分,取第4部分的中点作为阈值,此时基于Pearson和文本互信息的阈值模型将会有相近的边数,有利于这两种模型的对比.数据使用了沪深两地证券市场地区指数收盘价,时间从2006年1月4日至2016年12月30日,共计2673个交易日.从网络节点相关性看,基于文本互信息的方法能够体现出大约20%的非线性相关关系;在网络整体拓扑指标上,本文计算了4种指标,结果显示能够使所保留的节点联系更为紧密,有效提高保留节点的重要性以及挖掘出更好的社区结构;最后,计算了阈值网络的动态指标,将数据按年分别构建网络,缩减方法只用了阈值方法,结果显示本文提出的方法在小世界动态和网络度中心性等指标上能够成功捕捉到样本区间内存在的两次异常波动.此外,本文构建的地区金融网络具有服从幂律分布、动态稳定性、一些经济欠发达地区在金融地区网络中占据重要地位等特性.     

A study of the interplay between the structure variation and fluctuations of the Shanghai stock market

The intricate interplay between the variation of the stock network structure and fluctuations of that stock market is increasingly becoming a hot topic. In this work, employing a moving window to scan through every stock price time series over a period from 2 January 2001 to 7 December 2010, we use mutual information to measure the statistical interdependence between stock prices, and we construct a corresponding network for 501 Shanghai stocks in every given window. Then we address the time-varying relationships between the structure variation and fluctuations for the Shanghai stock market. All the results obtained here indicate that at turning points the growing independence of stocks causes the scalefreeness of the degree distribution to be disrupted, and that the Shanghai stock index has little volatility clustering. In contrast, under normality of the market, the stock networks have characteristics of scalefree degree distribution. Furthermore, the degree of volatility clustering is a little higher.     

Networks of equities in financial markets

We review the recent approach of correlation based networks of financial equities. We investigate portfolio of stocks at different time horizons, financial indices and volatility time series and we show that meaningful economic information can be extracted from noise dressed correlation matrices. We show that the method can be used to falsify widespread market models by directly comparing the topological properties of networks of real and artificial markets.Received: 26 November 2003, Published online: 14 May 2004PACS: 89.75.Fb Structures and organization in complex systems - 89.75.Hc Networks and genealogical trees - 89.65.Gh Economics; econophysics, financial markets, business and management     

Network formation in a multi-asset artificial stock market

A multi-asset artificial stock market is developed. In the market, stocks are assigned to a number of sectors and traded by heterogeneous investors. The mechanism of continuous double auction is employed to clear order book and form daily closed prices. Simulation results of prices at the sector level show an intra-sector similarity and inter-sector distinctiveness, and returns of individual stocks have stylized facts that are ubiquitous in the real-world stock market. We find that the market risk factor has critical impact on both network topology transition and connection formation, and that sector risk factors account for the formation of intra-sector links and sector-based local interaction. In addition, the number of community in threshold-based networks is correlated negatively and positively with the value of correlation coefficients and the ratio of intra-sector links, which are respectively determined by intensity of sector risk factors and the number of sectors.     

Deterministic factors of stock networks based on cross-correlation in financial market

The stock market has been known to form homogeneous stock groups with a higher correlation among different stocks according to common economic factors that influence individual stocks. We investigate the role of common economic factors in the market in the formation of stock networks, using the arbitrage pricing model reflecting essential properties of common economic factors. We find that the degree of consistency between real and model stock networks increases as additional common economic factors are incorporated into our model. Furthermore, we find that individual stocks with a large number of links to other stocks in a network are more highly correlated with common economic factors than those with a small number of links. This suggests that common economic factors in the stock market can be understood in terms of deterministic factors.     

Extracting hidden fluctuation patterns of Hang Seng stock index from network topologies

We present a model of complex network generated from Hang Seng index (HSI) of Hong Kong stock market, which encodes stock market relevant both interconnections and interactions between fluctuation patterns of HSI in the network topologies. In the network, the nodes (edges) represent all kinds of patterns of HSI fluctuation (their interconnections). Based on network topological statistic, we present efficient algorithms, measuring betweenness centrality (BC) and inverse participation ratio (IPR) of network adjacency matrix, for detecting topological important nodes. We have at least obtained three uniform nodes of topological importance, and find the three nodes, i.e. 18.7% nodes undertake 71.9% betweenness centrality and closely correlate other nodes. From these topological important nodes, we can extract hidden significant fluctuation patterns of HSI. We also find these patterns are independent the time intervals scales. The results contain important physical implication, i.e. the significant patterns play much more important roles in both information control and transport of stock market, and should be useful for us to more understand fluctuations regularity of stock market index. Moreover, we could conclude that Hong Kong stock market, rather than a random system, is statistically stable, by comparison to random networks.     

Dynamic structure of stock communities: a comparative study between stock returns and turnover rates

The detection of community structure in stock market is of theoretical and practical significance for the study of financial dynamics and portfolio risk estimation. We here study the community structures in Chinese stock markets from the aspects of both price returns and turnover rates, by using a combination of the PMFG and infomap methods based on a distance matrix. An empirical study using the overall data set shows that for both returns and turnover rates the largest communities are composed of specific industrial or conceptional sectors and the correlation inside a sector is generally larger than the correlation between different sectors. However, the community structure for turnover rates is more complex than that for returns, which indicates that the interactions between stocks revealed by turnover rates may contain more information. This conclusion is further confirmed by the analysis of the changes in the dynamics of community structures over five sub-periods. Sectors like banks, real estate, health care and New Shanghai take turns to comprise a few of the largest communities in different sub-periods, and more interestingly several specific sectors appear in the communities with different rank orders for returns and turnover rates even in the same sub-period. To better understand their differences, a comparison between the evolution of the returns and turnover rates of the stocks from these sectors is conducted. We find that stock prices only had large changes around important events while turnover rates surged after each of these events relevant to specific sectors, which shows strong evidence that the turnover rates are more susceptible to exogenous shocks than returns and its measurement for community detection may contain more useful information about market structure.     

Hierarchical structure in financial markets

I find a hierarchical arrangement of stocks traded in a financial market by investigating the daily time series of the logarithm of stock price. The topological space is a subdominant ultrametric space associated with a graph connecting the stocks of the portfolio analyzed. The graph is obtained starting from the matrix of correlation coefficient computed between all pairs of stocks of the portfolio by considering the synchronous time evolution of the difference of the logarithm of daily stock price. The hierarchical tree of the subdominant ultrametric space associated with the graph provides a meaningful economic taxonomy. Received 24 March 1999 and Received in final form 28 June 1999     

Information flow between composite stock index and individual stocks

We investigate the strength and the direction of information transfer in the US stock market between the composite stock price index of stock market and prices of individual stocks using the transfer entropy. Through the directionality of the information transfer, we find that individual stocks are influenced by the index of the market.     

Dynamic Analyses of Contagion Risk and Module Evolution on the SSE A-Shares Market Based on Minimum Information Entropy

The interactive effect is significant in the Chinese stock market, exacerbating the abnormal market volatilities and risk contagion. Based on daily stock returns in the Shanghai Stock Exchange (SSE) A-shares, this paper divides the period between 2005 and 2018 into eight bull and bear market stages to investigate interactive patterns in the Chinese financial market. We employ the Least Absolute Shrinkage and Selection Operator (LASSO) method to construct the stock network, compare the heterogeneity of bull and bear markets, and further use the Map Equation method to analyse the evolution of modules in the SSE A-shares market. Empirical results show that (1) the connected effect is more significant in bear markets than bull markets and gives rise to abnormal volatilities in the stock market; (2) a system module can be found in the network during the first four stages, and the industry aggregation effect leads to module differentiation in the last four stages; (3) some stocks have leading effects on others throughout eight periods, and medium- and small-cap stocks with poor financial conditions are more likely to become risk sources, especially in bear markets. Our conclusions are beneficial to improving investment strategies and making regulatory policies.     

Distinguishing manipulated stocks via trading network analysis

Manipulation is an important issue for both developed and emerging stock markets. For the study of manipulation, it is critical to analyze investor behavior in the stock market. In this paper, an analysis of the full transaction records of over a hundred stocks in a one-year period is conducted. For each stock, a trading network is constructed to characterize the relations among its investors. In trading networks, nodes represent investors and a directed link connects a stock seller to a buyer with the total trade size as the weight of the link, and the node strength is the sum of all edge weights of a node. For all these trading networks, we find that the node degree and node strength both have tails following a power-law distribution. Compared with non-manipulated stocks, manipulated stocks have a high lower bound of the power-law tail, a high average degree of the trading network and a low correlation between the price return and the seller-buyer ratio. These findings may help us to detect manipulated stocks.     

Cross-correlation matrix analysis of Chinese and American bank stocks in subprime crisis

In order to study the universality of the interactions among different markets, we analyze the cross-correlation matrix of the price of the Chinese and American bank stocks. We then find that the stock prices of the emerging market are more correlated than that of the developed market. Considering that the values of the components for the eigenvector may be positive or negative, we analyze the differences between two markets in combination with the endogenous and exogenous events which influence the financial markets. We find that the sparse pattern of components of eigenvectors out of the threshold value has no change in American bank stocks before and after the subprime crisis. However, it changes from sparse to dense for Chinese bank stocks. By using the threshold value to exclude the external factors, we simulate the interactions in financial markets.     

Evolution of networks

We review the recent rapid progress in the statistical physics of evolving networks. Interest has focused mainly on the structural properties of complex networks in communications, biology, social sciences and economics. A number of giant artificial networks of this kind have recently been created, which opens a wide field for the study of their topology, evolution, and the complex processes which occur in them. Such networks possess a rich set of scaling properties. A number of them are scale-free and show striking resilience against random breakdowns. In spite of the large sizes of these networks, the distances between most of their vertices are short - a feature known as the 'small-world' effect. We discuss how growing networks self-organize into scale-free structures, and investigate the role of the mechanism of preferential linking. We consider the topological and structural properties of evolving networks, and percolation and disease spread on these networks. We present a number of models demonstrating the main features of evolving networks and discuss current approaches for their simulation and analytical study. Applications of the general results to particular networks in nature are discussed. We demonstrate the generic connections of the network growth processes with the general problems of non-equilibrium physics, econophysics, evolutionary biology, and so on.     

Theoretical analyses of stock correlations affected by subprime crisis and total assets: Network properties and corresponding physical mechanisms

In the field of statistical mechanics and system science, it is acknowledged that the financial crisis has a profound influence on stock market. However, the influence of total asset of enterprise on stock quote was not considered in the previous studies. In this work, a modified cross-correlation matrix that focuses on the influence of total asset on stock quote is introduced into the analysis of the stocks collected from Asian and American stock markets, which is different from the previous studies. The key results are obtained as follows. Firstly, stock is more greatly correlated with big asset than with small asset. Secondly, the higher the correlation coefficient among stocks, the larger the eigenvector is. Thirdly, in different periods, like the pre-subprime crisis period and the peak of subprime crisis period, Asian stock quotes show that the component of the third eigenvector of the cross-correlation matrix decreases with the asset of the enterprise decreasing.Fourthly, by simulating the threshold network, the small network constructed by 10 stocks with large assets can show the large network state constructed by 30 stocks. In this research we intend to fully explain the physical mechanism for understanding the historical correlation between stocks and provide risk control strategies in the future.     

Detecting and Analyzing Politically-Themed Stocks Using Text Mining Techniques and Transfer Entropy—Focus on the Republic of Korea’s Case

Politically-themed stocks mainly refer to stocks that benefit from the policies of politicians. This study gave the empirical analysis of the politically-themed stocks in the Republic of Korea and constructed politically-themed stock networks based on the Republic of Korea’s politically-themed stocks, derived mainly from politicians. To select politically-themed stocks, we calculated the daily politician sentiment index (PSI), which means politicians’ daily reputation using politicians’ search volume data and sentiment analysis results from politician-related text data. Additionally, we selected politically-themed stock candidates from politician-related search volume data. To measure causal relationships, we adopted entropy-based measures. We determined politically-themed stocks based on causal relationships from the rates of change of the PSI to their abnormal returns. To illustrate causal relationships between politically-themed stocks, we constructed politically-themed stock networks based on causal relationships using entropy-based approaches. Moreover, we experimented using politically-themed stocks in real-world situations from the schematized networks, focusing on politically-themed stock networks’ dynamic changes. We verified that the investment strategy using the PSI and politically-themed stocks that we selected could benchmark the main stock market indices such as the KOSPI and KOSDAQ around political events.     

Response of scale-free networks with community structure to external stimuli

The response of scale-free networks with community structure to external stimuli is studied. By disturbing some nodes with different strategies, it is shown that the robustness of this kind of network can be enhanced due to the existence of communities in the networks. Some of the response patterns are found to coincide with topological communities. We show that such phenomena also occur in the cat brain network which is an example of a scale-free like network with community structure. Our results provide insights into the relationship between network topology and the functional organization in complex networks from another viewpoint.     

Spectrum,intensity and coherence in weighted networks of a financial market

We construct a correlation matrix based financial network for a set of New York Stock Exchange (NYSE) traded stocks with stocks corresponding to nodes and the links between them added one after the other, according to the strength of the correlation between the nodes. The eigenvalue spectrum of the correlation matrix reflects the structure of the market, which also shows in the cluster structure of the emergent network. The stronger and more compact a cluster is, the earlier the eigenvalue representing the corresponding business sector occurs in the spectrum. On the other hand, if groups of stocks belonging to a given business sector are considered as a fully connected subgraph of the final network, their intensity and coherence can be monitored as a function of time. This approach indicates to what extent the business sector classifications are visible in market prices, which in turn enables us to gauge the extent of group-behaviour exhibited by stocks belonging to a given business sector.     

Intraday volatility and network topological properties in the Korean stock market

We examine whether the relationship between market volatility and network properties in the low-frequency level can be applied to the high-frequency level. For the analysis, we use the minimum spanning tree (MST) method constructed from intraday Korean stock market data. The results show that the higher the market volatility is, the denser the MST of stocks becomes. The normalized tree length shows a strong negative relationship with market volatility, indicating that the distances between nodes are shorter when the market volatility is high. The mean occupation layer shows the tendency of having a smaller value in a higher volatility market. The maximum number of links becomes larger when the market volatility increases. All these network properties support the network being dense and shrinking in high market volatility conditions; that is, the degree of co-movement in financial market is reinforced in the intraday high-frequency level.     

Improving robustness of complex networks via the effective graph resistance

Improving robustness of complex networks is a challenge in several application domains, such as power grids and water management networks. In such networks, high robustness can be achieved by optimizing graph metrics such as the effective graph resistance, which is the focus of this paper. An important challenge lies in improving the robustness of complex networks under dynamic topological network changes, such as link addition and removal. This paper contributes theoretical and experimental findings about the robustness of complex networks under two scenarios: (i) selecting a link whose addition maximally decreases the effective graph resistance; (ii) protecting a link whose removal maximally increases the effective graph resistance. Upper and lower bounds of the effective graph resistance under these topological changes are derived. Four strategies that select single links for addition or removal, based on topological and spectral metrics, are evaluated on various synthetic and real-world networks. Furthermore, this paper illustrates a novel comparison method by considering the distance between the added or removed links, optimized according to the effective graph resistance and the algebraic connectivity. The optimal links are different in most cases but in close proximity.