Finite-Range Contact Process on the Market Return Intervals Distributions

Stochastic system is applied to describe and investigate the fluctuations of stock price changes in a stock market, and a stock price model is developed by the finite-range contact process of the statistical physics systems. In this paper, the scaling behaviors of the return intervals for SSE Composite Index (SSE) and the simulation data of the model are investigated and compared. The database is from the index of SSE in the 6-year period for every 5 minutes, and the simulation data is from the finite-range contact model for different values of the range R. For different values of threshold θ, the statistical analysis shows that the probability density function Pθ(τ) of the return intervals τ for both SSE and the simulation data have similar scaling form, that is Pθ(τ) = τ̄ −1h(τ/τ̄) (τ̄ is the mean return interval), where the scaling function h(x) can be approximately fitted by the function h(x) = ωe−a(lnx) γ , and ω, a, γ are three parameters. Further, with different values of R and θ, the statistical comparison of SSE Composite Index and simulation data are given.