Non Gaussian Models of Dependence in Returns

Abstract

Models of dependence in asset returns with non-Gaussian marginals are investigated on ETF daily return data. The first is a full rank Gaussian copula. The second is a linear mixture of independent Lévy processes. The third correlates Gaussian components in a variance gamma representation. On a number of occasions all three models are comparable. More generally we get a superior performance from the LM model followed by VGC and FGC. There are occasions when the VGC and FGC dominate. The concept of local correlation is introduced to help discriminate between the models and it is observed that the LM models displays higher levels of local correlation especially in the tails when compared to either VGC or LM.

Keywords: Gaussian Copula, Correlated Levy Process, Linear Mixture of Levy, Independent Components Analysis

JEL Classification: G1, G12, G13