Complex stock trading network among investors

arXiv:1003.2459v2 [q-fin.ST] 25 May 2010 Complex stock trading network among investors Zhi-Qiang Jianga,b,c, Wei-Xing Zhoua,b,c,d,∗ aSchool of Business, East China University of Science and Technology, Shanghai 200237, China bSchool of Science, East China University of Science and Technology, Shanghai 200237, China cResearch Center for Econophysics, East China University of Science and Technology, Shanghai 200237, China dResearch Center on Fictitious Economics & Data Science, Chinese Academy of Sciences, Beijing 100080, China Abstract We provide an empirical investigation aimed at uncovering the statistical properties of intricate stock trading networks based on the order flow data of a highly liquid stock (Shenzhen Development Bank) listed on Shenzhen Stock Ex- change during the whole year of 2003. By reconstructing the limit order book, we can extract detailed information of each executed order for each trading day and demonstrate that the trade size distributions for different trading days exhibit power-law tails and that most of the estimated power-law exponents are well within the L´evy stable regime. Based on the records of order matching among investors, we can construct a stock trading network for each trading day, in which the investors are mapped into nodes and each transaction is translated as a direct edge from the seller to the buyer with the trade size as its weight. We find that all the trading networks comprise a giant component and have power-law degree distributions and disassortative architectures. In particular, the degrees are correlated with order sizes by a power-law function. By regarding the size executed order as its fitness, the fitness model can reproduce the empirical power-law degree distribution. Keywords: Econophysics, limit order book, trade sizes, trading networks, power-law distribution PACS: 89.65.Gh, 89.75.Hc, 89.75.Da 1. Introduction Most people believe that the global economic and financial systems exhibit more and more remarkably intertwined nature with a continuing increase in economy globalization using different measures [1–7], although some measures give a different scenario [6, 8], which provides a diffusion path for the US subprime mortgage lending crisis triggering the current global financial and economic crisis, mainly in the developed economies [7]. There is no doubt that studying the structure and dynamics of financial and economic networks will provide revolutionary insights to our understanding of the evolution of financial and economic systems, which have predictive implication for policy makers [9]. The ideal picture would be that we have a unified network for all economic units and the detailed information of their interactions. Unfortunately, such a database is almost impossible to build. Nevertheless, the importance of network analysis of financial and economic systems is self-evident, especially in the Econophysics community. In recent years, complex network theory has witnessed a flourishing progress in many interdisciplinary natural and social fields [10–15]. Quite a few network patterns differing from random graphs have been revealed, such as small world [10, 16], scale-free degree distribution [11], community [17–20], and rich club [21–23], to list a few. Complex financial and economic networks can be classified in three categories. In the first category of networks, the nodes present financial or economic agents (economies, companies, financial institutions, traders, et al) and a link is drawn between two nodes if they have certain interactions (such as investment, trade, lending, economic cooperation, et al) [24–35]. In the second category of networks, the nodes are agents, each of which has a time series recording ∗Corresponding author. Address: 130 Meilong Road, P.O. Box 114, School of Business, East China University of Science and Technology, Shanghai 200237, China, Phone: +86 21 64253634, Fax: +86 21 64253152. Email address: wxzhou@ecust.edu.cn (Wei-Xing Zhou ) Preprint submitted to Physica A June 20, 2021 its behavior and a link is drawn due to the correlation between two time series [36–42]. The third category contains networks converted from individual financial time series [43–47], based on different mapping methods such as phase space embedding, visibility algorithm, sub-series correlation, recurrence, and n-tuple occurrence [48–55]. The complex financial and economic networks of first type range from the macroscopic level of countries to the microscopic level of traders in markets. Trading networks at the microscopic are less studied, since the detailed information of trader identities and their transactions is usually unavailable to researchers with merely a few excep- tions. Kyriakopoulos et al have investigated the statistical properties of the transaction network of all major financial players (423 accounts) within Austria over one year [56]. They found that the directed network is disassortative and the random matrix analysis is able to identify an acco

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