Modeling and simulation of the market fluctuations by the finite range contact systems

In this paper, we model a new random stock price model for the stock markets based on the finite range contact process, which is a model for epidemic spreading that mimics the interplay of local infections and recovery of individuals, it is a member of a class of stochastic processes known as interacting particle systems. Then, we analyze the statistical behaviors of Shanghai Stock Exchange (SSE) Composite Index, Shenzhen Stock Exchange (SZSE) Composite Index, Dow Jones Industrial Average Index (DJIA), Nasdaq Composite Index (IXIC), the standard and Poor’s 500 Index (S&P500) and the simulative data derived from the finite range contact model by comparison. And six individual Chinese stocks from large-cap, mid-cap and small-cap categories are discussed. Furthermore, we investigate the long range correlations of the returns for these indices and the corresponding simulative data by applying the detrended fluctuation analysis. At last, the positive part of the probability distributions of the logarithmic returns for the actual data and the simulative data are studied by the q-Gaussian dynamic systems. The main objective of this work is to discuss the impact on the returns with the different range financial models.