Interaction Structure And Large-volatility Dynam-ics In Complex Financial Systems

In recent years, there has been a growing interest of physicists in complex economic and social systems. Financial markets are such important and representative examples with many-body interactions, somewhat similar to traditional physical systems. With large amounts of historical data piled up in the past years, it becomes possible to analyze the col-lective behavior of financial markets based on concepts and methods in statistical physics. To some extent, the collective behavior of the financial dynamics is rather robust, indepen-dent of particular stock markets, at least within the mature markets in western countries. On the other hand, it is also known that the emerging markets may behave differently. Es-pecially, the Chinese stock market is newly set up in1990and shares a transiting economic and social system. Up to date, however, the dynamic behavior of the emerging markets is much less concerned, compared with that of the mature markets. Therefore, we focus on the comparative study of Chinese and western stock markets, and explore the universal and non-universal dynamic behavior of the Chinese stock market. Furthermore, as a modern trend in interdisciplines, econophysics is not only generating a subfield in physics, but also leading to quantitative study of financial systems with advanced techniques.From the view of statistical physics, one may compute the time and spatial correlation functions for understanding the stationary state of a dynamic system. These correlation functions could be derived with phenomenological methods and/or from fundamental mi-croscopic interactions. At this stage, it is natural that only the dynamic properties averaged over time or individual stocks or’many’events are practically concerned. In econophysics, economic and financial significance should be also taken into account. In this article, we will proceed in such a line. Chapter3,4,5is the main results of our work.In Chapter1, the history of the financial market, especially the stock market is intro-duced briefly. As one of the most important emerging markets, the evolution of the chinese stock market are presented. Particularly, we give a brief introduction to the development of the econophysics, which describes the financial dynamics with the statistical physics. The main approaches are random matrix theory, complex networks and time-correlation function. Finally, we show the research motivation and the main research content.In Chapter2, we give a brief introduction to the dynamics of financial system. It includes the statistical properties, temporal correlations and stochastic model of price dy-namics. Several significant universal and non-universal dynamics behavior are presented. We also pay attention in experiments in laboratories,i.e., the behavioral finance, which simulates the financial and economic systems.In Chapter3, we study the spatial structure of the Chinese stock market, American stock market and global market indices, with the random matrix theory. After taking into account the signs of the components in the eigenvectors of the cross-correlation matrix, we detect the subsector structure of the financial systems. The positive and negative subsectors are anti-correlated each other in the corresponding eigenmode. The subsector structure is strong in the Chinese stock market, while somewhat weaker in the American stock market and global market indices. Characteristics of the subsector structures in different markets are revealed.In Chapter4, we investigate the interaction structure of communities in financial mar-kets, with the network methods and random matrix theory. In particular, based on the ran-dom matrix decomposition, we clarify that the local interactions between the business sec-tors (subsectors) are mainly contained in the sector mode. In the sector mode, the average correlation inside the sectors is positive, while that between the sectors is negative. Fur-ther, we explore the time evolution of the interaction structure of the business sectors, and observe that the local interaction structure changes dramatically during a financial bubble or crisis.In Chapter5, we investigate the large-fluctuation dynamics in financial markets, based on the minute-to-minute and daily data of the Chinese Indices and German DAX. The dy-namic relaxation both before and after the large fluctuations is characterized by a power law, and the exponents p±usually vary with the strength of the large fluctuations. The large-fluctuation dynamics is time-reversal symmetric at the time scale in minutes, while asymmetric at the daily time scale. Careful analysis reveals that the time-reversal asym-metry is mainly induced by external forces. It is also the external forces which drive the financial system to a non-stationary state. Different characteristics of the Chinese and Ger-man stock markets are uncovered.In Chapter6, the main conclusions of this dissertation are summarized.