In this article fractal scale exponent estimation approach using Continuous Wavelet Transform is considered. The goal of this article is to provide adequate fractal scale exponent estimation approach for financial time series data in capital markets using wavelet transforms. This approach should be beneficial for the most European and Asia stock index forecasting simulations. In order to identify European and Asia stock index multiracial scaling exponent spectrum, Wavelet Transform Modulus Maxima (WTMM) method is being used for skeleton function estimation; multifractal formalism is checked using Fractal Partition Function, which is analysed using Moment Generating Function, consequently Local Scaling Exponents Spectrum is calculated. Multifractal Local Scaling Exponents Spectrum is parameterized with other methods. In this article most European and Asia stock indexes are considered. Objects of experiment are 9 worldwide stock indexes: Dow Jones Industrial Average, AEX, CAC40, DAX30, IBEX, FTSE100, Nikkei225, SMI, STI. The Dow Jones Industrial Average index is considered for the whole available period: from 01/01/1900 to 01/04/2012, other mentioned indexes were analyzed during the following period: 05/07/1993 to 01/04/2012. In this research World Stock Indexes multifractal nature is analysed.