Light to equity indexes analysis is given using wavelet transforms (Direct Continuous Wavelet transform and Inverse Continuous Wavelet transform as well as Direct Discrete Wavelet Transform and Inverse Discrete Wavelet Transform). Direct Continuous Wavelet Transform has been used as a tool to describe some properties of equity indexes such as Hurts exponent, wavelet coefficients probability distribution, pseudo frequencies on a certain scaling parameters. Most of them are essential to find significant changes in equity index behavior and predict instability. Some variations of Fractal Brownian Motion are proposed in current article; as a result the stochastic process with “dynamic” Hurts exponent is defined. Some algorithms for process simulation by using Direct and Inverse Continuous Wavelet Transforms via “Morlet” mother wavelet function are provided within article. Proposed variations of Fractal Brownian Motion are beneficial for equity index simulations with variant return indicators on various investment horizons