Multivariate subordination of stable processes

TL;DR

This paper explores multivariate stable processes with time-changed models, highlighting their advantages over Brownian motions for financial data, especially when using transaction counts as stochastic time, through multivariate subordination and Lévy copulas.

Contribution

It introduces a detailed model combining multivariate subordination and Lévy copulas, enhancing the modeling of stock prices with transaction-based stochastic time changes.

Findings

More accurate stock price modeling with transaction-based time changes

Advantages over classical Brownian motion models

Use of Lévy copulas for dependence structure

Abstract

This article is devoted to some time-changed stochastic models based on multivariate stable processes. The considered models have several advantages in comparison with classical time-changed Brownian motions - for instance, it turns out that they are more appropriate for describing stock prices if the amount of transactions is used for a stochastic time change. In this paper, we provide a detailed discussion of the model, which is based on two popular concepts - multivariate subordination and L{\'e}vy copulas.