Empirical Analysis Of The High-frequency Data And The Multi-agent Models Of Stock Markets

The study of the dynamics of the stock markets is a popular research field and much attention of the scientists from different fields has been drawn to it. The stock market is a complex dynamic system with multibody interactions. It has some statistical properties as many other physical complex systems, e.g., long-range correlation, self-similarity, and universality. Using the concepts and methods from statistical physics, we try to study the microstructure of the stock markets based on the analysis of the high-frequency data and construct multi-agent models simulating the financial dynamics. This interdisciplinary field is called Econophysics.In Chapter 1, we firstly give an overview of the background of the Econophysics, including a short historic review of the stock markets, the emergence of Econophysics and its inverse contribution to physics. Then we introduce the present focus on the study of the financial markets, e.g., the empirical analysis of the high-frequency stock series and multi-agent models.In Chapter 2, we investigate the statistical properties of the German DAX and Chinese indices, including the volatility distribution, autocorrelation function, DFA function, and the return-volatility correlation function. 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 autocorrelation function of the Chinese indices shows different dynamic behavior from the German DAX. By investigating the return-volatility correlation function, we observe a leverage effect for the German DAX, while an antileverage effect for the Chinese indices for both the daily data and minutely data. A retarded volatility model may describe the asymmetric properties of the financial indices. My colleagues and I finished the work in this chapter, and I did the main work in Chapters 3,4,5 under the construction of my supervisor.In Chapter 3, we present a relatively detailed analysis of the persistence probability distributions and introduce a nonlocal description of the return-volatility correlation. Compared with the autocorrelation function, the persistence probability distributions describe dynamic correlations nonlocal in time. Universal and nonuniversal behaviors of the German DAX and Shanghai Stock Exchange Composite Index are analyzed using the daily data and minutely data. The persistence probability at fixed point z0= 0 is further generalized to the case z0≠0. The observation of the return-volatility correlation function nonlocal in time confirms the behavior of the return-volatility correlation function local in time in the positive time direction. An antileverage effect of the volatility-return correlation nonlocal in time is detected for both the German DAX and Chinese indices in the negative time direction.In Chapter 4, in order to remove intrinsic periodicity of the standard minority game (MG), and make it more comparable to the financial markets, we introduce the score-dependent and agent-dependent payoffs of the strategies into the MG model. Thus the characteristics of the stock markets arise, such as long-range volatility correlations and "fat tails" in the distribution of returns. The agent dependence of the payoffs is essential in producing the long-range volatility correlations. The new payoffs lead to a better performance in the dynamic behavior nonlocal in time, and can coexist with the inactive strategy. We also observe that the standard deviationσ2/N is significantly reduced, thus the efficiency of the system is distinctly improved. Based on this observation, we give a qualitative explanation for the long-range volatility correlations. Furthermore, we introduce the score-dependent and agent-dependent payoffs to the thermal MG model, and find it plays an important role in producing long-range volatility correlations. This indicates that the new payoffs bring a nontrivial dynamic mechanism to the MGs.In Chapter 5, in order to capture the long-range volatility correlations and other characteristics of the stock markets, the feed-back interactions are introduced to the EZ herding models. Empirical study shows that the volatility and trading volume as well as other variables of the stock market are considered to be highly correlated with the price formalism of the stock markets. We introduce herding models with feed-back interactions in terms of volatility and trading volume separately. For the model with volatility interaction, transmission of information at time t'is supposed to depend on the volatility of the financial index at t'-1. Both static and dynamic behaviors are investigated, i.e., the return distribution, the volatility autocorrelation function, zero return distribution and the persistence probability. Furthermore, the recently discovered two-phase phenomenon in financial markets is examined with the German DAX, and it can be correctly produced by this interacting herding model. For the model with trading volume interaction, each agent trades with a probability which is supposed to depend on his/her own trading volume at his/her last trade. The price return is determined according to the volume imbalance and the number of trades. The model could reproduce the power-law distributions of the financial fluctuations, i.e., price returns, trading volume and the number of trades, and their relations. The generated time series are also long-range correlated.