Lévy-stability-under-addition and fractal structure of markets: Implications for the investment management industry and emphasized examination of MATIF notional contract

This paper presents the connection between the stable distributions and the fractal structure of markets. After having described the main concepts, we conduct an emphasized empirical examination of the Lévy-stability-under-addition of the French MATIF notional contract on ten year government bonds. Following Mandelbrotʹs intuitions, we attempt to verify the existence of an underlying fractal structure governing the price variations, on different time intervals. The results are in the sense of Mandelbrotʹs intuitions: it is possible to characterize a fractal structure from one to 20 days variations (returns) of the market. This fractal structure is only perceptible using the Lévy distributions, and in this sense, the fractality of the market is associated with the Lévy-stability-under-addition property. By rescaling space and time, the statistical invariance of MATIF is exhibited. Implications of the results are given for the investment process and investment management industry.