Procesos de Lévy y algunas aplicaciones en las finanzas

Abstract

Asset prices have been modeled mainly by Wiener processes since 1900. In recent years, many works have observed difficulties in the statistical properties of the asset returns because it does not come from a normal distribution as believed, due to the high kurtosis and heavy tails, which generally are caused by sudden changes (jumps) of the asset prices. Therefore, this work presents an introduction to Lévy processes which are a class of stochastic processes provided with independent and stationary increments, the cádlág property, infinitely divisible distributions and other generic properties which allow a better modeling of the assets prices, because they can represent the pathwise jumps of assets prices and their distributions.