Multivariate Variance Gamma and Gaussian dependence: a study with copulas

This paper explores the dynamic dependence properties of a Lévy process, the Variance Gamma, which has non Gaussian marginal features and non Gaussian dependence. In a static context, such a non Gaussian dependence should be represented via copulas. Copulas, however, are not able to capture the dynamics of dependence. By computing the distance between the Gaussian copula and the actual one, we show that even a non Gaussian process, such as the Variance Gamma, can ”converge” to linear dependence over time. Empirical versions of different dependence measures confirm the result. Journal of Economic Literature Classification: C16, G12. Elisa Luciano University of Turino. P.za Arbarello, 8, 10122 Turin. ICER and Collegio Carlo Alberto. e-mail: [email protected] Patrizia Semeraro University of Turino. P.za Arbarello, 8, 10122 Turin, e-mail: [email protected] ∗ March 2008. c © 2008 by Elisa Luciano and Patrizia Semeraro. Any opinions expressed here are those of the authors and not those of Collegio Carlo Alberto. We thank Claudio Patrucco for having provided the marginal calibrations and Ksenia Rulik for computational assistance. Financial support from MIUR is gratefully acknowledged.