No Stable Distributions in Finance, please!

TL;DR

This paper argues against the common assumption that heavy-tailed stable distributions, like the Cauchy, accurately model financial data, by highlighting the discrepancy in observed outliers.

Contribution

It challenges the justification for using stable distributions in finance by demonstrating the mismatch between expected and observed outliers in real data.

Findings

Fewer outliers are observed in financial data than predicted by stable distributions.

Cauchy and symmetric stable distributions do not match the outlier patterns in actual financial indexes.

The main argument for heavy-tailed models in finance is fundamentally flawed.

Abstract

Failure of the main argument for the use of heavy tailed distribution in Finance is given. More precisely, one cannot observe so many outliers for Cauchy or for symmetric stable distributions as we have in reality. keywords:outliers; financial indexes; heavy tails; Cauchy distribution; stable distributions