Modelling tail risk with tempered stable distributions: an overview

In this study, we investigate the performance of different parametric models with stable and tempered stable distributions for capturing the tail behaviour of log-returns (financial asset returns). First, we define and discuss the properties of stable and tempered stable random variables. We then show how to estimate their parameters and simulate them based on their characteristic functions. Finally, as an illustration, we conduct an empirical analysis to explore the performance of different models representing the distributions of log-returns for the S&P500 and DAX indexes.

Automated summary

This study investigates the performance of different parametric models using stable and tempered stable distributions for capturing the tail behavior of log-returns. It defines and discusses the properties of stable and tempered stable random variables, shows how to estimate parameters and simulate them based on characteristic functions, and conducts an empirical analysis to explore the performance of different models representing the distributions of log-returns for the S&P500 and DAX indexes.