Multivariate non-Gaussian models for financial applications

TL;DR

This paper reviews and analyzes several multivariate non-Gaussian models for financial data, focusing on their properties, calibration, and empirical performance on stock index returns.

Contribution

It provides a comprehensive analysis of recent multivariate non-Gaussian models, including their features, characteristic functions, moments, and calibration methods for financial applications.

Findings

Models exhibit diverse dependence structures and parameter efficiencies.

Calibration methods are practical for real-world log-return data.

Empirical comparison highlights strengths and limitations of each model.

Abstract

In this paper we consider several continuous-time multivariate non-Gaussian models applied to finance and proposed in the literature in the last years. We study the models focusing on the parsimony of the number of parameters, the properties of the dependence structure, and the computational tractability. For each model we analyze the main features, we provide the characteristic function, the marginal moments up to order four, the covariances and the correlations. Thus, we describe how to calibrate them on the time-series of log-returns with a view toward practical applications and possible numerical issues. To empirically compare these models, we conduct an analysis on a five-dimensional series of stock index log-returns.