Some Contra-Arguments for the Use of Stable Distributions in Financial Modeling

TL;DR

This paper critically examines the limitations of Pareto-Levy distributions in financial modeling, highlighting their inability to account for observed outliers and questioning their theoretical foundations, and proposes alternative approaches.

Contribution

It provides a critical analysis of Pareto-Levy distributions in finance and suggests alternative modeling strategies.

Findings

Pareto-Levy distributions lack sufficient outliers in real data

Connection with classical limit theorem is questionable

Proposes alternative modeling approaches

Abstract

In the present paper, we discuss contra-arguments concerning the use of Pareto-Lev\'y distributions for modeling in Finance. It appears that such probability laws do not provide sufficient number of outliers observed in real data. Connection with the classical limit theorem for heavy-tailed distributions with such type of models is also questionable. The idea of alternative modeling is given.