Mandelbrot Fractal Market Model Analysis

This paper studies a new model of stock time series introduced by Benoit Mandelbrot in 1997 which is based on the use of fractals. An important tool of this model is the Hurst parameter H which is linked to the fractal dimension and also shows whether time series have long time independence or not. This paper will first introduce the classic models and then the new model of Mandelbrot and make their comparisons; the improbable is thus better estimated in the Mandelbrot model. This paper also applies the Rescaled range (R/S) analysis of Hurst onto Chinese stocks and international indices and exchanges rates in order to have practical results and to put into relief these dependences. Thus, we can see that for most of the cases, the Hurst parameter is bigger than 0.5, moreover, it appears that this parameter is decreasing with the time. Looking at 20 calendar days, the dependence tends to vanish, market is so becoming independent up to this period. A final part of this paper focuses on the study of the relevance of the Hurst parameter to predict future behavior. It appears that its information is not enough to anticipate future evolutions.