Self-similarity in the analysis of financial markets' behaviour

Relying on self-similarities and scale invariances, scientists have started to think about financial markets as complex dynamical systems, and to use techniques imported from physics. The purpose of this essay is to present an overview and an application of this approach. A simple dynamical system, similar in principle to Tartaglia’s triangle, is found to produce a self-similar structure. The scaling-invariant properties of power law and Lévy-stable distributions are then exposed. Eight data sets of historical prices are analyzed to provide evidence of the superiority of Lévy-stable distributions over Gaussian ones in describing price fluctuations statistically