Multivariate tempered stable additive subordination for financial models

TL;DR

This paper introduces multivariate tempered stable Sato subordinators to model additive, time-inhomogeneous processes with dynamic correlations, improving financial data fit.

Contribution

It presents a novel class of Sato subordinators for multivariate tempered stable distributions, enabling better modeling of correlation dynamics in financial data.

Findings

The processes exhibit time-dependent correlation structures.

The models fit financial data well.

Numerical illustrations demonstrate correlation dynamics.

Abstract

We study a class of multivariate tempered stable distributions and introduce the associated class of tempered stable Sato subordinators. These Sato subordinators are used to build additive inhomogeneous processes by subordination of a multiparameter Brownian motion. The resulting process is additive and time inhomogeneous. Furthermore, these processes are associated with the distribution at unit time of a class of L\'evy process with good fit properties on fifinancial data. The main feature of the Sato subordinated Brownian motion is that it has time dependent correlation, whereas the L\'evy counterpart does not. We provide a numerical illustration of the correlation dynamics.