Simulating financial markets indexes with generalized WMF model

It is diffiult to simulate the dynamical behaviour of actual fiancial markets indexes effctively, especially when they have nonlinear characteristics. So to propose a mathematical model with these characteristics is important. In this paper, we investigate a generalized Weierstrass-Mandelbrot function (WMF) model with two nonlinear characteristics: fractal dimension 2 > D > 1.5 and hurstexponent (H) where 1 > H > 0.5 firstly. And then we study its dynamical behaviour as D and H change in 3-dimensional space. Basing on these results, we simulate diffrent stocks markets indexes such as Daily Dow Johns index and Daily S&P 500 index. Using the fiting line method in 2-dimensional space for the simulated values and diffrent actual stock markets indexes, we fi d that the generalized WMF model is effctive for simulating diff rent actual stock markets indexes in diffrent time ranges. It may be useful for understanding the dynamical behaviour of many di ffrent fiancial markets.