Three Non-Gaussian Models of Dependence in Returns

Three particular models of dependence in asset returns with non-Gaussian marginals are investigated on daily return data for sector exchange traded funds. The first model is a full rank Gaussian copula (FGC). The second models returns as a linear mixture of independent Levy processes (LML). The third correlates Gaussian components in a variance gamma representation (VGC). On a number of occasions all three models are comparable. More generally, in some by sectors, we get a superior performance from the LML model followed by VGC and FGC as measured by the proportion of portfolios with higher p-values. 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 LML models display higher levels of local correlation especially in the tails when compared with either the VGC or FGC models.