| The influence of financial markets is becoming prominent since a continually-growing amount of economic activities trading all over the global, and different fields of scientists have been engaged on the study of financial markets besides economists. On the other hand, the theory of complex systems, investigate the macroscopic laws emerged when numerous individuals self-organize to an ensemble through non-linear interactions between them. Financial market is a typical complex system. Therefore, it is available to study financial markets based on the theory of complex systems, statistical physics, applied mathematics, etc, and this research field has blossomed into a branch of learning, called econophysics. In this study, we aim our research on the dynamic properties of financial markets using theory of complex systems and statistical physics. It consists of three aspects:1. We study the stock price fluctuations of7developed and emerging financial markets, adopting the measurement of She-Leveque (SL) hierarchy from turbulence.The SL hierarchy, which was projected to characterize the anomalous scaling law in velocity fluctuations in fluid turbulence, provides a concise measurement to describe multi-fractality and nonlinear scaling law, with only three parameters:the intermittent parameter β, the most high intensity scaling exponent ho and the codimension C. Since the financial market and turbulence have been broadly compared on account of the same quantitative methods and several common stylized facts they share, the SL hierarchical structures model is applied here to study and quantify the hierarchical structure of stock price fluctuations. Several interesting results are observed:(i) The hierarchical structure related to multifractal scaling generally presents in all the7stock price fluctuations;(ii) The quantitatively statistical parameters that describe SL hierarchy are different between developed financial markets and emerging markets, distinctively;(iii) For the high-frequency stock price fluctuation, the hierarchical structure varies with different time periods. These results increase the analogies between the turbulence and financial market dynamics, and provide a profound understanding beyond the phenomenological description of multifractal scaling in stock price fluctuations, and thus may help us to better model the dynamic evolution of financial markets based on multiple cascade processes.2. Regarding the financial markets as a complex network, in which the nodes represent the stocks and corresponding companies, we study the static topological structure and dynamical evolution of the networks to obtain the relationship between the stock price fluctuations and financial crisis. A series of dynamic correlation-based financial networks are constructed by winner-take-all approach and sliding window technology, with both dynamic and static threshold values. By analyzing the three global parameters, average degree, average shortest path length, and average cluster coefficient evolving in a14-year period, we find that the financial networks show a robust small-world property. Furthermore, the irregularities of curves indicating the dynamic evolution of financial network highly associate with the economic crashes. These results may provide a novel view of complex network science to deeply understand the origin of financial crisis.3. To study the dynamic process and the statistical properties of financial markets, we build up a simplified artificial financial markets model including investors and investments. In our model, the investors, according to their selection capabilities, are regarded as active or passive, considering the fact that every investor can only perceive partial information to make right decisions. Meanwhile, the investments can be good or bad defined by their qualities. The good investments have a larger probability to attract investors, with higher cost yet. An interesting result is derived that without any external influence, the system can self-organized evolve to a quasi-stationary stable by the interaction between investors and investments according to their own strategies. Moreover, the partial information asymmetry of financial market and various qualities of investments commonly result in a diversity of investors’and investments’dynamic behaviors. This study verifies that the dynamics of a stock market is comparable with that of an evolutionary ecology such as the population of biological species, and that the financial market can be referred to as the ecological system, thus may give vital clues to investigate the financial market ecology. |
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