Stochastic Interacting Financial Market System Volatility Behavior And Statistical Analysis

With the rapid development of capital securitization process and the continual im-provement of the rapidly changing Internet having been promoting financial reform and innovation, financial market is developing quickly, more and more investors partici-pate in the operation of the financial market. To research the financial phenomena and behaviors has been a significant approach and method to comprehend the initial for-mation mechanism and operation rules. The interaction among market participants is one important reason of giving rise to the fluctuations of the financial market prices, depending on this factor, stochastic interacting spin models are as the very important statistical physics models, using them to analyze the microstructure of financial market has been widely acknowledged. In our paper, Ising dynamic model and Potts model are used to develop the financial price models to detect some price formation and spreading mechanism. After that, Matlab software is applied to obtain some numerical modeling series, and those series are with different parameters. This work is to make preparations for the latter statistical analysis.For the different return time series derived from Ising model and Potts model, em-pirical mode decomposition is used to receive corresponding intrinsic mode function series for the former, and adopting duration analysis to transform return series into volatility duration series. Nowadays, complex network analysis has become a popular research field, so visibility graph and horizontal visibility graph are applied to translate financial series into assortative networks. Then in the view of degree point, some kind of "degree" methods such as degree distribution, assortative mixing pattern, hierarchy and so on are used in our paper.As a significant role in the paper, the empirical analysis is indispensable, by con-trast. So Hang Seng Index (HSI), Shanghai Composite Index (SSE) and Shenzhen Component Index (SZSE) are chosen to be researched by those statistical approaches applied in simulation series. After that, the proposed price models depending on Ising and Potts are reasonable to some extent.