Series representations for bivariate time-changed L{\'e}vy models

TL;DR

This paper develops a series representation for a bivariate Lévy process model that combines subordination and Lévy copulas, enabling efficient simulation and practical data analysis.

Contribution

It introduces a novel series representation for bivariate time-changed Lévy models using Lévy copulas, facilitating simulation and application.

Findings

Series representation enables efficient simulation.

Practical examples demonstrate model applicability.

Model captures dependence via Lévy copulas.

Abstract

In this paper, we analyze a L{\'e}vy model based on two popular concepts - subordination and L{\'e}vy copulas. More precisely, we consider a two-dimensional L{\'e}vy process such that each component is a time-changed (subordinated) Brownian motion and the dependence between subordinators is described via some L{\'e}vy copula. We prove a series representation for our model, which can be efficiently used for simulation purposes, and provide some practical examples based on real data