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.     

Preferred numbers and the distributions of trade sizes and trading volumes in the Chinese stock market

The distributions of trade sizes and trading volumes are investigated based on the limit order book data of 22 liquid Chinese stocks listed on the Shenzhen Stock Exchange in the whole year 2003. We observe that the size distribution of trades for individualstocks exhibits jumps, which is caused by the number preference of traders when placing orders. We analyze the applicability of the “q-Gamma” function for fitting the distribution by the Cramér-von Mises criterion. The empirical PDFs of tradingvolumes at different timescales Δt ranging from 1 min to 240 min can be well modeled. The applicability of the q-Gamma functions for multiple trades is restricted to the transaction numbers Δn≤ 8. We find that all the PDFs have power-law tails for large volumes. Using careful estimation of the average tail exponents α of the distributions of trade sizes and trading volumes, we get α> 2, well outside the Lévy regime.     

Crowded Trades,Market Clustering,and Price Instability

Crowded trades by similarly trading peers influence the dynamics of asset prices, possibly creating systemic risk. We propose a market clustering measure using granular trading data. For each stock, the clustering measure captures the degree of trading overlap among any two investors in that stock, based on a comparison with the expected crowding in a null model where trades are maximally random while still respecting the empirical heterogeneity of both stocks and investors. We investigate the effect of crowded trades on stock price stability and present evidence that market clustering has a causal effect on the properties of the tails of the stock return distribution, particularly the positive tail, even after controlling for commonly considered risk drivers. Reduced investor pool diversity could thus negatively affect stock price stability.     

Empirical study of recent Chinese stock market

We investigate the statistical properties of the empirical data taken from the Chinese stock market during the time period from January, 2006 to July, 2007. By using the methods of detrended fluctuation analysis (DFA) and calculating correlation coefficients, we acquire the evidence of strong correlations among different stock types, stock index, stock volume turnover, A share (B share) seat number, and GDP per capita. In addition, we study the behavior of “volatility”, which is now defined as the difference between the new account numbers for two consecutive days. It is shown that the empirical power-law of the number of aftershock events exceeding the selected threshold is analogous to the Omori law originally observed in geophysics. Furthermore, we find that the cumulative distributions of stock return, trade volume and trade number are all exponential-like, which does not belong to the universality class of such distributions found by Xavier Gabaix et al. [Xavier Gabaix, Parameswaran Gopikrishnan, Vasiliki Plerou, H. Eugene Stanley, Nature, 423 (2003)] for major western markets. Through the comparison, we draw a conclusion that regardless of developed stock markets or emerging ones, “cubic law of returns” is valid only in the long-term absolute return, and in the short-term one, the distributions are exponential-like. Specifically, the distributions of both trade volume and trade number display distinct decaying behaviors in two separate regimes. Lastly, the scaling behavior of the relation is analyzed between dispersion and the mean monthly trade value for each administrative area in China.     

A unified econophysics explanation for the power-law exponents of stock market activity

We survey a theory (first sketched in Nature in 2003, then fleshed out in the Quarterly Journal of Economics in 2006) of the economic underpinnings of the fat-tailed distributions of a number of financial variables, such as returns and trading volume. Our theory posits that they have a common origin in the strategic trading behavior of very large financial institutions in a relatively illiquid market. We show how the fat-tailed distribution of fund sizes can indeed generate extreme returns and volumes, even in the absence of fundamental news. Moreover, we are able to replicate the individually different empirical values of the power-law exponents for each distribution: 3 for returns, 3/2 for volumes, 1 for the assets under management of large investors. Large investors moderate their trades to reduce their price impact; coupled with a concave price impact function, this leads to volumes being more fat-tailed than returns but less fat-tailed than fund sizes. The trades of large institutions also offer a unified explanation for apparently disconnected empirical regularities that are otherwise a challenge for economic theory.     

Characteristics of real futures trading networks

Futures trading is the core of futures business, and it is considered as one of the typical complex systems. To investigate the complexity of futures trading, we employ the analytical method of complex networks. First, we use real trading records from the Shanghai Futures Exchange to construct futures trading networks, in which nodes are trading participants, and two nodes have a common edge if the two corresponding investors appear simultaneously in at least one trading record as a purchaser and a seller, respectively. Then, we conduct a comprehensive statistical analysis on the constructed futures trading networks. Empirical results show that the futures trading networks exhibit features such as scale-free behavior with interesting odd-even-degree divergence in low-degree regions, small-world effect, hierarchical organization, power-law betweenness distribution, disassortative mixing, and shrinkage of both the average path length and the diameter as network size increases. To the best of our knowledge, this is the first work that uses real data to study futures trading networks, and we argue that the research results can shed light on the nature of real futures business.     

Power law and multiscaling properties of the Chinese stock market

We investigate the cumulative probability density function (PDF) and the multiscaling properties of the returns in the Chinese stock market. By using returns data adjusted for thin trading, we find that the distribution has power-law tails at shorter microscopic timescales or lags. However, the distribution follows an exponential law for longer timescales. Furthermore, we investigate the long-range correlation and multifractality of the returns in the Chinese stock market by the DFA and MFDFA methods. We find that all the scaling exponents are between 0.5 and 1 by DFA method, which exhibits the long-range power-law correlations in the Chinese stock market. Moreover, we find, by MFDFA method, that the generalized Hurst exponents h(q) are not constants, which shows the multifractality in the Chinese stock market. We also find that the correlation of Shenzhen stock market is stronger than that of Shanghai stock market.     

Modeling interactions of trading volumes in financial dynamics

A dynamic herding model with interactions of trading volumes is introduced. At time t, an agent trades with a probability, which depends on the ratio of the total trading volume at time t−1 to its own trading volume at its last trade. The price return is determined by the volume imbalance and number of trades. The model can reproduce the power-law distributions of the trading volume, number of trades and price return, and the probable relation between them. The exponents are tunable by adjusting the values of the parameters, but show slight deviation from those revealed in empirical studies. Moreover, the time series generated are long-range correlated. We demonstrate that the results are rather robust, and do not depend on the particular form of the trading probability.     

Recursive weighted treelike networks

We propose a geometric growth model for weighted scale-free networks, which is controlled by two tunable parameters. We derive exactly the main characteristics of the networks, which are partially determined by the parameters. Analytical results indicate that the resulting networks have power-law distributions of degree, strength, weight and betweenness, a scale-free behavior for degree correlations, logarithmic small average path length and diameter with network size. The obtained properties are in agreement with empirical data observed in many real-life networks, which shows that the presented model may provide valuable insight into the real systems.     

General dynamics of topology and traffic on weighted technological networks

For most technical networks, the interplay of dynamics, traffic, and topology is assumed crucial to their evolution. In this Letter, we propose a traffic-driven evolution model of weighted technological networks. By introducing a general strength-coupling mechanism under which the traffic and topology mutually interact, the model gives power-law distributions of degree, weight, and strength, as confirmed in many real networks. Particularly, depending on a parameter W that controls the total weight growth of the system, the nontrivial clustering coefficient C, degree assortativity coefficient r, and degree-strength correlation are all consistent with empirical evidence.     

Stylized facts from a threshold-based heterogeneous agent model

A class of heterogeneous agent models is investigated where investors switch trading position whenever their motivation to do so exceeds some critical threshold. These motivations can be psychological in nature or reflect behaviour suggested by the efficient market hypothesis (EMH). By introducing different propensities into a baseline model that displays EMH behaviour, one can attempt to isolate their effects upon the market dynamics. The simulation results indicate that the introduction of a herding propensity results in excess kurtosis and power-law decay consistent with those observed in actual return distributions, but not in significant long-term volatility correlations. Possible alternatives for introducing such long-term volatility correlations are then identified and discussed.     

Fitness-dependent topological properties of the world trade web

Among the proposed network models, the hidden variable (or good get richer) one is particularly interesting, even if an explicit empirical test of its hypotheses has not yet been performed on a real network. Here we provide the first empirical test of this mechanism on the world trade web, the network defined by the trade relationships between world countries. We find that the power-law distributed gross domestic product can be successfully identified with the hidden variable (or fitness) determining the topology of the world trade web: all previously studied properties up to third-order correlation structure (degree distribution, degree correlations, and hierarchy) are found to be in excellent agreement with the predictions of the model. The choice of the connection probability is such that all realizations of the network with the same degree sequence are equiprobable.     

Local Events and Dynamics on Weighted Complex Networks

We examine the weighted networks grown and evolved by local events, such as the addition of new vertices and links and we show that depending on frequency of the events, a generalized power-law distribution of strength can emerge. Continuum theory is used to predict the scaling function as well as the exponents, which is in good agreement with the numerical simulation results. Depending on event frequency, power-law distributions of degree and weight can also be expected. Probability saturation phenomena for small strength and degree in many real world networks can be reproduced. Particularly, the non-trivial clustering coefficient, assortativity coefficient and degree-strength correlation in our model are all consistent with empirical evidences.     

Weighted Networks Model Based on Traffic Dynamics with Local Perturbation

In the study of weighted complex networks, the interplay between traffic and topology have been paid much attention. However, the variation of topology and weight brought by new added vertices or edges should also be considered. In this paper, an evolution model of weighted networks driven by traffic dynamics with local perturbation is proposed. The model gives power-law distribution of degree, weight and strength, as confirmed by empirical measurements. By choosing appropriate parameters W and δ, the exponents of various power law distributions can be adjusted to meet real world networks. Nontrivial clustering coefficient C, degree assortativity coefficient r, and strength-degree correlation are also considered. What should be emphasized is that, with the consideration of local perturbation, one can adjust the exponent of strength-degree correlation more effectively. It makes our model more general than previous ones and may help reproducing real world networks more appropriately. PACS numbers： 87.23.Kg, 89.75.Da, 89.75.Fb, 89.75.Hc.     

Tuning degree distributions: Departing from scale-free networks

Scale-free networks are characterized by a degree distribution with power-law behavior. Although scale-free networks have been shown to arise in many areas, ranging from the World Wide Web to transportation or social networks, degree distributions of other observed networks often differ from the power-law type. Data based investigations require modifications of the typical scale-free network.We present an algorithm that generates networks in which the shape of the degree distribution is tunable by modifying the preferential attachment step of the Barabási-Albert construction algorithm. The shape of the distribution is represented by dispersion measures such as the variance and the skewness, both of which are highly correlated with the maximal degree of the network and, therefore, adequately represents the influence of superspreaders or hubs. By combining our algorithm with work of Holme and Kim, we show how to generate networks with a variety of degree distributions and clustering coefficients.     

An evolving model of online bipartite networks

Understanding the structure and evolution of online bipartite networks is a significant task since they play a crucial role in various e-commerce services nowadays. Recently, various attempts have been tried to propose different models, resulting in either power-law or exponential degree distributions. However, many empirical results show that the user degree distribution actually follows a shifted power-law distribution, the so-called Mandelbrot’s law, which cannot be fully described by previous models. In this paper, we propose an evolving model, considering two different user behaviors: random and preferential attachment. Extensive empirical results on two real bipartite networks, Delicious and CiteULike  , show that the theoretical model can well characterize the structure of real networks for both user and object degree distributions. In addition, we introduce a structural parameter p$p$, to demonstrate that the hybrid user behavior leads to the shifted power-law degree distribution, and the region of power-law tail will increase with the increment of p$p$. The proposed model might shed some lights in understanding the underlying laws governing the structure of real online bipartite networks.     

Pyramid scheme in stock market:A kind of financial market simulation

Artificial stock market simulation based on agent is an important means to study financial market. Based on the assumption that the investors are composed of a main fund, small trend and contrarian investors characterized by four parameters, we simulate and research a kind of financial phenomenon with the characteristics of pyramid schemes. Our simulation results and theoretical analysis reveal the relationships between the rate of return of the main fund and the proportion of the trend investors in all small investors, the small investors' parameters of taking profit and stopping loss,the order size of the main fund and the strategies adopted by the main fund. Our work is helpful to explain the financial phenomenon with the characteristics of pyramid schemes in financial markets, design trading rules for regulators and develop trading strategies for investors.     

A Collaboration Network Model with Multiple Evolving Factors

To describe the empirical data of collaboration networks,several evolving mechanisms have been proposed,which usually introduce different dynamics factors controlling the network growth.These models can reasonably reproduce the empirical degree distributions for a number of well-studied real-world collaboration networks.On the basis of the previous studies,in this work we propose a collaboration network model in which the network growth is simultaneously controlled by three factors,including partial preferential attachment,partial random attachment and network growth speed.By using a rate equation method,we obtain an analytical formula for the act degree distribution.We discuss the dependence of the act degree distribution on these different dynamics factors.By fitting to the empirical data of two typical collaboration networks,we can extract the respective contributions of these dynamics factors to the evolution of each networks.     

Betweenness centrality in finite components of complex networks

We use generating function formalism to obtain an exact formula of the betweenness centrality in finite components of random networks with arbitrary degree distributions. The formula is obtained as a function of the degree and the component size, and is confirmed by simulations for Poisson, exponential, and power-law degree distributions. We find that the betweenness centralities for the three distributions are asymptotically power laws with an exponent 1.5 and are invariant to the particular distribution parameters.     

用户需求行为对互联网动力学整体特性的影响

由Internet构成的复杂网络的动力学特性主要受到用户需求行为的影响,具备时域的统计规律性. 通过对区域群体用户需求行为的时域实验统计分析,发现用户对Web网站的访问频度及其生成的二分网络的入度分布也呈现幂律分布和集聚现象,其幂指数介于1.7到1.8之间. 建立了虚拟资源网络VRN和物理拓扑网络PTN双层模型,分析了双层模型映射机理,并对网络用户需求行为进行建模. 虚拟资源网络VRN对物理拓扑网络PTN映射过程的不同机理,模拟了Internet资源网络到物理网络的不同影响模式. 幂律分布的用户需求特性会 关键词： 复杂网络 无标度拓扑 用户需求 相变