The purpose of this article is to show that the correlation smile in liquid CDS index tranches can be explained by the same ideas that have explained the volatility smile in equity options. First, we extend a structural model proposed by Luciano and Schoutens [2005] that models firm values by Variance Gamma processes. We show that these extensions can explain the index spread curves and tranche quotes of DJ iTraxx 5 year simultaneously. Second, we extract the resulting dependence structure into a factor copula approach. The resulting VG copula shares the advantages of the well known Gaussian copula that underlies the most important industry models, such as CreditMetrics and KMV. We apply this approach to weekly spreads of DJ iTraxx 5 year. We show that this approach fits significantly better to the correlation smile than comparable copula approaches.