Tempered stable distributions and processes

TL;DR

This paper explores tempered stable distributions and processes, focusing on their densities, limit behaviors, parameter estimation, and applications in financial modeling.

Contribution

It provides new insights into the properties, density transformations, and $p$-variation indices of tempered stable processes, including their use in exponential stock models.

Findings

Analysis of limit distributions and densities

Parameter estimation methods for tempered stable distributions

Application to exponential stock models

Abstract

We investigate the class of tempered stable distributions and their associated processes. Our analysis of tempered stable distributions includes limit distributions, parameter estimation and the study of their densities. Regarding tempered stable processes, we deal with density transformations and compute their $p$-variation indices. Exponential stock models driven by tempered stable processes are discussed as well.