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This paper introduces a multivariate pure-jump Lévy process which allows for skewness and excess kurtosis of single asset returns and for asymptotic tail dependence in the multivariate setting. It is termed Variance Compound Gamma (VCG). The novelty of my approach is that, by applying a two-stage stochastic time change to Brownian motions, I derive a hierarchical structure with different properties of inter-and intra-sector dependence. I investigate the properties of the implied static copuladoi:10.2139/ssrn.1973040 fatcat:df47ywlhgzdbrh72wo3ynyly4u