A network analysis of the Chinese stock market

In many practical important cases, a massive dataset can be represented as a very large network with certain attributes associated with its vertices and edges. Stock markets generate huge amounts of data, which can be use for constructing the network reflecting the market’s behavior. In this paper, we use a threshold method to construct China’s stock correlation network and then study the network’s structural properties and topological stability. We conduct a statistical analysis of this network and show that it follows a power-law model. We also detect components, cliques and independent sets in this network. These analyses allows one to apply a new data mining technique of classifying financial instruments based on stock price data, which provides a deeper insight into the internal structure of the stock market. Moreover, we test the topological stability of this network and find that it displays a topological robustness against random vertex failures, but it is also fragile to intentional attacks. Such a network stability property would be also useful for portfolio investment and risk management.     

Evolution of Cohesion between USA Financial Sector Companies before,during, and Post-Economic Crisis: Complex Networks Approach

Various mathematical frameworks play an essential role in understanding the economic systems and the emergence of crises in them. Understanding the relation between the structure of connections between the system’s constituents and the emergence of a crisis is of great importance. In this paper, we propose a novel method for the inference of economic systems’ structures based on complex networks theory utilizing the time series of prices. Our network is obtained from the correlation matrix between the time series of companies’ prices by imposing a threshold on the values of the correlation coefficients. The optimal value of the threshold is determined by comparing the spectral properties of the threshold network and the correlation matrix. We analyze the community structure of the obtained networks and the relation between communities’ inter and intra-connectivity as indicators of systemic risk. Our results show how an economic system’s behavior is related to its structure and how the crisis is reflected in changes in the structure. We show how regulation and deregulation affect the structure of the system. We demonstrate that our method can identify high systemic risks and measure the impact of the actions taken to increase the system’s stability.     

Influence of a network structure on the network effect in the communication service market

In this study, we analyze the network effect in a model of a personal communication market, by using a multi-agent based simulation approach. We introduce into the simulation model complex network structures as the interaction patterns of agents. With complex network models, we investigate the dynamics of a market in which two providers are competing. We also examine the structure of networks that affect the complex behavior of the market. By a series of simulations, we show that the structural properties of complex networks, such as the clustering coefficient and degree correlation, have a major influence on the dynamics of the market. We find that the network effect is increased if the interaction pattern of agents is characterized by a high clustering coefficient, or a positive degree correlation. We also discuss a suitable model of the interaction pattern for reproducing market dynamics in the real world, by performing simulations using real data of a social network.     

Comparing the structure of an emerging market with a mature one under global perturbation

In this paper we investigate the Tehran stock exchange (TSE) and Dow Jones Industrial Average (DJIA) in terms of perturbed correlation matrices. To perturb a stock market, there are two methods, namely local and global perturbation. In the local method, we replace a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series, whereas in the global method, we reconstruct the correlation matrix after replacing the original return series with Gaussian-distributed time series. The local perturbation is just a technical study. We analyze these markets through two statistical approaches, random matrix theory (RMT) and the correlation coefficient distribution. By using RMT, we find that the largest eigenvalue is an influence that is common to all stocks and this eigenvalue has a peak during financial shocks. We find there are a few correlated stocks that make the essential robustness of the stock market but we see that by replacing these return time series with Gaussian-distributed time series, the mean values of correlation coefficients, the largest eigenvalues of the stock markets and the fraction of eigenvalues that deviate from the RMT prediction fall sharply in both markets. By comparing these two markets, we can see that the DJIA is more sensitive to global perturbations. These findings are crucial for risk management and portfolio selection.     

Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient

In this study, we first build two empirical cross-correlation matrices in the US stock market by two different methods, namely the Pearson’s correlation coefficient and the detrended cross-correlation coefficient (DCCA coefficient). Then, combining the two matrices with the method of random matrix theory (RMT), we mainly investigate the statistical properties of cross-correlations in the US stock market. We choose the daily closing prices of 462 constituent stocks of S&P 500 index as the research objects and select the sample data from January 3, 2005 to August 31, 2012. In the empirical analysis, we examine the statistical properties of cross-correlation coefficients, the distribution of eigenvalues, the distribution of eigenvector components, and the inverse participation ratio. From the two methods, we find some new results of the cross-correlations in the US stock market in our study, which are different from the conclusions reached by previous studies. The empirical cross-correlation matrices constructed by the DCCA coefficient show several interesting properties at different time scales in the US stock market, which are useful to the risk management and optimal portfolio selection, especially to the diversity of the asset portfolio. It will be an interesting and meaningful work to find the theoretical eigenvalue distribution of a completely random matrix R for the DCCA coefficient because it does not obey the Mar?enko–Pastur distribution.     

Principal regression analysis and the index leverage effect

We revisit the index leverage effect, that can be decomposed into a volatility effect and a correlation effect. We investigate the latter using a matrix regression analysis, that we call ‘Principal Regression Analysis’ (PRA) and for which we provide some analytical (using Random Matrix Theory) and numerical benchmarks. We find that downward index trends increase the average correlation between stocks (as measured by the most negative eigenvalue of the conditional correlation matrix), and makes the market mode more uniform. Upward trends, on the other hand, also increase the average correlation between stocks but rotates the corresponding market mode away from uniformity. There are two time scales associated to these effects, a short one on the order of a month (20 trading days), and a longer time scale on the order of a year. We also find indications of a leverage effect for sectorial correlations as well, which reveals itself in the second and third mode of the PRA.     

The string prediction models as invariants of time series in the forex market

In this paper we apply a new approach of string theory to the real financial market. The models are constructed with an idea of prediction models based on the string invariants (PMBSI). The performance of PMBSI is compared to support vector machines (SVM) and artificial neural networks (ANN) on an artificial and a financial time series. A brief overview of the results and analysis is given. The first model is based on the correlation function as invariant and the second one is an application based on the deviations from the closed string/pattern form (PMBCS). We found the difference between these two approaches. The first model cannot predict the behavior of the forex market with good efficiency in comparison with the second one which is, in addition, able to make relevant profit per year. The presented string models could be useful for portfolio creation and financial risk management in the banking sector as well as for a nonlinear statistical approach to data optimization.     

Idiosyncratic risk in the Dow Jones Eurostoxx50 Index

Recent evidence by Campbell et al. [J.Y. Campbell, M. Lettau B.G. Malkiel, Y. Xu, Have individual stocks become more volatile? An empirical exploration of idiosyncratic risk, The Journal of Finance (February) (2001)] shows an increase in firm-level volatility and a decline of the correlation among stock returns in the US. In relation to the Euro-Area stock markets, we find that both aggregate firm-level volatility and average stock market correlation have trended upwards.We estimate a linear model of the market risk–return relationship nested in an EGARCH(1, 1)-M model for conditional second moments. We then show that traditional estimates of the conditional risk–return relationship, that use ex-post excess-returns as the conditioning information set, lead to joint tests of the theoretical model (usually the ICAPM) and of the Efficient Market Hypothesis in its strong form.To overcome this problem we propose alternative measures of expected market risk based on implied volatility extracted from traded option prices and we discuss the conditions under which implied volatility depends solely on expected risk. We then regress market excess-returns on lagged market implied variance computed from implied market volatility to estimate the relationship between expected market excess-returns and expected market risk.We investigate whether, as predicted by the ICAPM, the expected market risk is the main factor in explaining the market risk premium and the latter is independent of aggregate idiosyncratic risk.     

Isospectral Twirling and Quantum Chaos

We show that the most important measures of quantum chaos, such as frame potentials, scrambling, Loschmidt echo and out-of-time-order correlators (OTOCs), can be described by the unified framework of the isospectral twirling, namely the Haar average of a k-fold unitary channel. We show that such measures can then always be cast in the form of an expectation value of the isospectral twirling. In literature, quantum chaos is investigated sometimes through the spectrum and some other times through the eigenvectors of the Hamiltonian generating the dynamics. We show that thanks to this technique, we can interpolate smoothly between integrable Hamiltonians and quantum chaotic Hamiltonians. The isospectral twirling of Hamiltonians with eigenvector stabilizer states does not possess chaotic features, unlike those Hamiltonians whose eigenvectors are taken from the Haar measure. As an example, OTOCs obtained with Clifford resources decay to higher values compared with universal resources. By doping Hamiltonians with non-Clifford resources, we show a crossover in the OTOC behavior between a class of integrable models and quantum chaos. Moreover, exploiting random matrix theory, we show that these measures of quantum chaos clearly distinguish the finite time behavior of probes to quantum chaos corresponding to chaotic spectra given by the Gaussian Unitary Ensemble (GUE) from the integrable spectra given by Poisson distribution and the Gaussian Diagonal Ensemble (GDE).     

The predictive performance of a path-dependent exotic-option credit risk model in the emerging market

Most empirical research of the path-dependent, exotic-option credit risk model focuses on developed markets. Taking Taiwan as an example, this study investigates the bankruptcy prediction performance of the path-dependent, barrier option model in the emerging market. We adopt Duan’s (1994) [11], (2000) [12] transformed-data maximum likelihood estimation (MLE) method to directly estimate the unobserved model parameters, and compare the predictive ability of the barrier option model to the commonly adopted credit risk model, Merton’s model. Our empirical findings show that the barrier option model is more powerful than Merton’s model in predicting bankruptcy in the emerging market. Moreover, we find that the barrier option model predicts bankruptcy much better for highly-leveraged firms. Finally, our findings indicate that the prediction accuracy of the credit risk model can be improved by higher asset liquidity and greater financial transparency.     

Structure of a financial cross-correlation matrix under attack

We investigate the structure of a perturbed stock market in terms of correlation matrices. For the purpose of perturbing a stock market, two distinct methods are used, namely local and global perturbation. The former involves replacing a correlation coefficient of the cross-correlation matrix with one calculated from two Gaussian-distributed time series while the latter reconstructs the cross-correlation matrix just after replacing the original return series with Gaussian-distributed time series. Concerning the local case, it is a technical study only and there is no attempt to model reality. The term ‘global’ means the overall effect of the replacement on other untouched returns. Through statistical analyses such as random matrix theory (RMT), network theory, and the correlation coefficient distributions, we show that the global structure of a stock market is vulnerable to perturbation. However, apart from in the analysis of inverse participation ratios (IPRs), the vulnerability becomes dull under a small-scale perturbation. This means that these analysis tools are inappropriate for monitoring the whole stock market due to the low sensitivity of a stock market to a small-scale perturbation. In contrast, when going down to the structure of business sectors, we confirm that correlation-based business sectors are regrouped in terms of IPRs. This result gives a clue about monitoring the effect of hidden intentions, which are revealed via portfolios taken mostly by large investors.     

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.     

Spot foreign exchange market and time series

We investigate high frequency price dynamics in foreign exchange market using data from Reuters information system (the dataset has been provided to us by Olsen and Associates). In our analysis we show that a naïve approach to the definition of price (for example using the spot mid price) may lead to wrong conclusions on price behavior as for example the presence of short term correlations for returns. For this purpose we introduce an algorithm which only uses the non arbitrage principle to estimate real prices from the spot ones. The new definition leads to returns which are not affected by spurious correlations. Furthermore, any apparent information (defined by using Shannon entropy) contained in the data disappears.Received: 12 June 2003, Published online: 9 September 2003PACS: 89.65.Gh Economics; econophysics, financial markets, business and management - 65.40.Gr Entropy and other thermodynamical quantities     

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.     

基于节点拓扑特征的中国基金公司共持网络持股行为波动相关性

选取2003—2012年期间半年度中国基金公司持上市公司股票份额面板数据为样本数据,以基金公司为节点,以同一时刻共持同一家上市公司股票关系为边,以同一时刻共持的上市公司数量为权重,构建中国基金公司共持关系结构等价加权网络(简称共持网络).结合统计物理学等方法,分析了共持网络的拓扑结构稳定性及具有不同拓扑特征值的节点随时间演变过程中与共持网络中三类节点集合持股行为波动相关性.三类节点集合分别为t-1时刻基于某一股票形成的共持关系完全连通子图节点集合(第一类节点集合)、t-1时刻共持网络中非完全连通子图的节点集合(第二类节点集合)、t时刻新进入共持网络的节点集合(第三类节点集合).分析结果显示:1)节点与第二类节点集合持股行为波动呈正相关,且相关系数随着节点集聚系数的增强而增大;2)只有当节点的度和点强度值较高时,节点与第一类和第二类节点集合的持股行为呈正相关;3)不同拓扑特征条件下的节点与第三类节点集合的持股行为均不存在波动相关性.本文提供了一个研究持股行为相关性的新思路,并为进一步研究股票市场结构等价网络及节点重要性差异提供了基础.     

Characteristics of the Korean stock market correlations

We establish in this study a network structure of the Korean stock market, one of the emerging markets, with its minimum spanning tree through the correlation matrix. Based on this analysis, it is found that the Korean stock market does not form the clusters of the business sectors or of the industry categories. When the MSCI (Morgan Stanley Capital International Inc.) index is exploited, we find that the clusters of the Korean stock market is formed. This finding implicates that the Korean market, in this context, is characteristically different from the mature markets.     

一类任意m×n阶矩形网络的电特性

任意矩形电路网络中的电位分布问题一直是科学研究的难题.本研究发展了研究电阻网络的递推-变换(RT)理论使之能够用于计算任意m×n阶电路网络模型.研究了一类含有任意边界的m×n阶矩形网络的电位分布及等效电阻,这是一个之前一直没有解决的深刻问题,因为之前的研究依赖于规则的边界条件或一个含有零电阻的边界条件.其他方法如格林函数技术和拉普拉斯矩阵方法计算电位函数比较困难,研究含有任意边界的电阻网络也是不可能的.电位函数问题是自然科学和工程技术领域研究的一个重要内容,如拉普拉斯方程的求解问题就是其中之一.本文给出了含有一条任意边界的m×n矩形电阻网络的节点电位函数解析式,并且得到了任意两节点间的等效电阻公式,同时导出了一些特殊情形下的结果.在对不同结果的比较研究时,得到了一个新的数学分式恒等式.     

Identifying the structure of group correlation in the Korean financial market

We investigate the structure of the cross-correlation in the Korean stock market. We analyze daily cross-correlations between price fluctuations of 586 different Korean stock entities for the 6-year time period from 2003 to 2008. The main purpose is to investigate the structure of group correlation and its stability by undressing the market-wide effect using the Markowitz multi-factor model and the network-based approach. We find the explicit list of significant firms in the few largest eigenvectors from the undressed correlation matrix. We also observe that each contributor is involved in the same business sectors. The structure of group correlation can not remain constant during each 1-year time period with different starting points, whereas only two largest eigenvectors are stable for 6 years 8-9 eigenvectors remain stable for half-year. The structure of group correlation in the Korean financial market is disturbed during a sufficiently short time period even though the group correlation exists as an ensemble for the 6-year time period in the evolution of the system. We verify the structure of group correlation by applying a network-based approach. In addition, we examine relations between market capitalization and businesses. The Korean stock market shows a different behavior compared to mature markets, implying that the KOSPI is a target for short-positioned investors.     

An analysis of cross-correlations in an emerging market

We apply random matrix theory to compare correlation matrix estimators C$C$ obtained from emerging market data. The correlation matrices are constructed from 10 years of daily data for stocks listed on the Johannesburg stock exchange (JSE) from January 1993 to December 2002. We test the spectral properties of C$C$ against random matrix predictions and find some agreement between the distributions of eigenvalues, nearest neighbour spacings, distributions of eigenvector components and the inverse participation ratios for eigenvectors. We show that interpolating both missing data and illiquid trading days with a zero-order hold increases agreement with RMT predictions. For the more realistic estimation of correlations in an emerging market, we suggest a pairwise measured-data correlation matrix. For the data set used, this approach suggests greater temporal stability for the leading eigenvectors. An interpretation of eigenvectors in terms of trading strategies is given, as opposed to classification by economic sectors.     

奇异值分解用于可调谐二极管激光吸收光谱技术去除系统噪声

可调谐二极管激光吸收光谱(TDLAS)技术用于气体浓度检测时,会受到谐波检测中基线漂移及噪声的影响,因此如何去除系统噪声一直是研究的热点。分析了连续截断信号和构造hankel矩阵两种不同方法下,奇异值分解(SVD)对TDLAS系统检测的理论意义。将二次谐波信号分别用该方法进行矩阵化排列和奇异值分解,选取适当阈值将部分奇异值置零并重构矩阵,得到了这两种方法对基线纠漂和去噪的不同效果。实验证明,奇异值分解方法不需加入额外系统部件、不需通零气扣除背景,就能够快速有效地去除TDLAS系统噪声,而构造hankel矩阵的方法适用于去除高频噪声,连续截断信号的方法适用于进行基线纠漂。将该方法应用于实际TDLAS系统氨气检测时的二次谐波,系统噪声去除率达80%。