Phenomenological Analysis And Model Study Of Financial Dynamics

A financial market is a large-scale'complex system' which continuously generates an enormous amount of high-frequency data series, and consequently evolves dynamically. Such a complex dynamic system has drawn the physicists' interest. On the other hand, the financial markets can also be regarded as a many-body system composed of many agents and other elements such as the brokers, market-makers. From the view of many-body systems, interactions among agents and producers may generate long-range temporal correlations in the financial dynamics, and therefore result in the so-called dynamic scaling behavior.In Chapter 1 we introduce the probability theory and the basic notion, also some useful distributions. In Chapter 2 we give an overview of the progress achieved on econophysics in the recent years, including the phenomenological analysis such as the probability distribution, the autocorrelation function, the two-phase phenomenon and the leverage effect, and the advanced modeling approaches, such as the evolutionary game theory, percolation models and their variants, and the limit-order driven models based on the continuous double auction.In Chapter 3 we investigate statistical properties of the German DAX and Chinese indices, including the volatility distribution, autocorrelation function and DFA function, with both the daily data and minutely data. At the daily time scale, the volatility distribution, autocorrelation function and DFA function of the Chinese indices are qualitatively similar to those of the German Dax. At the minutely time scale, the auto-correlation function and DFA function of the Chinese indices behave differently from those of the German DAX due to irregular noises from the environment.In Chapter 4 we investigate the return-volatility correlation functions of the German DAX and Chinese indices, with both the daily data and minutely data. It is found the return-volatility correlation function of the Chinese Indices exhibits an anti-leverage effect, different from the standard leverage effect of the German Dax. Such a phenomenon is further explored with correlation functions non-local in time. More interestingly, in the negative time direction, the anti-leverage effect non-local in time is detected for both the German and Chinese markets, although the duplicate local in time does not exist. Numerical simulations of the leverage and anti-leverage effects are also presented.In Chapter 5 we develop an interacting EZ herding model. In application to the financial dynamics, transmission of information at time t' is supposed to depend on the variation of the financial index at time t'-1. The generated time series is strongly correlated in time at criticality. The dynamic behavior of the interacting EZ herding model is investigated. We study the two phase behavior of the German Dax. In particularly, we are interested in the relation between the two-phase behavior and the "volatility clustering". By a comparative study of the minority games and the EZ herding model it is observed that the two phase behavior and the long-range volatility autocorrelation are two independent characteristics. Compared with the minority games and the EZ herding model, the interacting EZ herding model correctly produces the two-phase phenomenon.In Chapter 6 we investigate a limit-order driven SM model. We perform numerical simulations of the limit-order driven SM model, aiming at understanding statistical properties of the bid-ask spread and the quote-update frequency. The probability distribution and autocorrelation function of the bid-ask spread S are analyzed. We also investigate the correlations among the spread S, volatility| Z| and absolute value of the mid-quote change|M| . The probability distribution and the autocorrelation of the quote-update frequency U are also discussed. The results of the SM model are qualitatively consistent with those of the empirical study.