Fluctuation Behavior Of Stochastic-Ising Financial Dynamical System

As the globalization and the Internet grow rapidly, the financial market is develop-ing fast and penetrating to all aspects of daily life. To understand the mechanism and characteristics of financial markets from the microscopic structure is becoming a key problem in risk management and market fluctuation. A complex behavior can emerge due to the interactions among smallest components of that system, and it is often a successful strategy to analyze the behavior of a complex system by studying these com-ponents. Thus, an interacting-agent model, which based on the stochastic Ising dynamic system, is considered in this thesis to explain price formation in financial markets. The corresponding returns time series are also defined. By computer simulation and numer-ically study, it also shows that Ising model can duplicate main factors of asset returns, such as fat-tail phenomenon, power-law behavior of tail distribution, long memory of absolute returns and multifractal spectrum of returns. By the financial market formed from Ising type, the interaction in Ising dynamic model presents fresh conceptual in-sight into dynamic and reciprocal relations in financial systems. The success of this interdisciplinary modeling implies that there is a physical common ground in nature that is open to exploration. This thesis includes the following seven parts:In Chapter1, a brief introduction of background and current researches in econo-physics has been given. And the innovation of our study is also presented.In Chapter2, the origin and development of Ising dynamic system, the definition and behavior of two dimensional Ising system, and how it is applied into financial mar-ket.In Chapter3, price formation in financial markets based on the two-dimensional stochastic Ising-like spin model is proposed, with a randomized inverse temperature of each trading day. The statistical behaviors of returns of this financial model are in-vestigated for zero boundary condition and five different classes of mixed boundary conditions. Different boundary conditions represent different investment environment. For comparison with actual financial markets, we also analyze the statistical properties of returns time series from Shanghai Stock Exchange (SSE) composite Index, Shen-zhen Stock Exchange (SZSE) component Index and Hushen300Index. With the plus boundary condition, the value of market depth parameter y is smaller than those of the corresponding market depth parameters y with free boundary condition ?1and weak mixed boundary conditions ?2and ?3. And the changing range of tails exponents of boundary condition ?6is much smaller than those of the other five boundary conditions.In Chapter4, we devoted to do researches on the effect of volatilities of financial returns by Stochastic Ising dynamic model. We also compare our results with the past22years of Chinese stock market, and find that there exits a critical point to distinguish large and small risk in stock market. From the microstructure of this model, we explain how volatility changes and which may gives some inspires on the risk management of financial market.In Chapter5, a financial market model is deveploped using an Ising spin system on a Sierpinski carpet lattice that breaks the equal status of each spin. To study the fluc-tuation behavior of the financial model, we present numerical research based on Monte Carlo simulation in conjunction with the statistical analysis and multifractal analysis of the financial time series. We extract the multifractal spectra by selecting various lattice size values of the Sierpinski carpet, and the inverse temperature of the Ising dy-namic system. We also investigate the statistical fluctuation behavior, the time-varying volatility clustering, and the multifractality of returns for the indices SSE, SZSE, DJIA, IXIC, S&P500, HSI, N225, and for the simulation data derived from the Ising model on Sierpinski carpet lattice. A numerical study of the model's dynamical properties reveals that this financial model reproduces important features of the empirical data.In Chapter6, an interacting-agent model of speculative activity explaining price formation in financial markets is considered, which based on the stochastic Ising model and the mean field theory. The model describes the interaction strength among the agents as well as an external field, and the corresponding random logarithmic price re-turn process is investigated. According to the numerical research of the model, the time series formed by this Ising model exhibits the bursting typical of volatility clustering, the fat-tail phenomenon, the power-law distribution tails and the long-time memory. Further, the multifractal detrended fluctuation analysis is applied to investigate the time series returns simulated by Ising model have the distribution multifractality as well as the correlation multifractality.In Chapter7, Summary of this thesis and the future work.