Analisi della struttura frattale del mercato finanziario italiano

The standard hypothesis on Normal (or Log-normal) distribution of the variations of the stock returns seems to be not verified in empirical works. In particular, many outliers, unstationarity in the variance level and asymmetry suggest the use of a Pareto-Lévy stable probability distribution. In our work, we have estimated the four parameters of this distribution for some time series concerning both stock market indexes and securities of the Italian stock market. These estimates lead to formulate the conjecture that the stochastic process generating the analysed stock returns be characterized by a fractal structure. In order to check this conjecture, we have empirically verified that the random variable concerning stock returns shows the property of statistical self-similarity, that is one of the properties of the fractal objects. Finally, we have empirically verified the property of invariance with respect to the sum (under the hypothesis of independence of the random variables), property characterizing only this family of distributions.