Stochastic Continuous Financial Price Model And Volatility Duration Statistical Analysis

Multi-continuum percolation system is one of the important particle systems in Econophysics,which offers an important direction for studying the construction of complex and nonlinear financial stock price model.In this paper,we firstly modify the two-dimensional multi-continuum percolation model.We introduce different radius parameters and a new ratio parameter to represent different abilities to spread informa-tion of investors,which is the basis of constructing two-dimensional multi-continuum percolation financial price model.The basic assumption is that the price fluctuations in stock markets are caused by the spread of investment information,wherefore it is of the essence to model the different abilities of investors to spread the information.Furthermore,three-dimensional multi-continuum percolation financial price model is put forward,which provides a new train of thought and tactics for exploring the price fluctuations in stock markets.We simulate these two financial price models by Mat-lab software.We attain the stock price series and corresponding return series.In this paper,we transform the price series and return series into volatility duration series,intrinsic mode functions and volatility series,and therefore we investigate the statis-tical properties of the financial price models.Firstly,we focus on the volatility dura-tion analyses of two-dimensional multi-continuum percolation financial price model,including multifractal detrending moving average analysis and Zipf analysis.We find that the simulation data has similar multifractal behaviors and Zipf distribution as re-al stock markets.Meanwhile,cross recurrence quantification analysis and multiscale cross-sample entropy analysis are applied to investigate the synchrony properties of the three-dimensional multi-continuum percolation financial price model,which shows similar synchrony behaviors as real markets.And therefore the proposed models are reasonable to model financial markets,to some extent.In this paper,two stock indexes of China,including SSE and SZSE,are applied to carry out the same statistical analyses as comparison,which is used to testify the rationality and the effectiveness of the proposed models.