  We unify and extend a number of approaches related to constructing
multivariate Variance-Gamma (V.G.) models for option pricing. An overarching
model is derived by subordinating multivariate Brownian motion to a
subordinator from the Thorin (1977) class of generalised Gamma convolution
subordinators. A class of models due to Grigelionis (2007), which contains the
well-known Madan-Seneta V.G. model, is of this type, but our multivariate
generalization is considerably wider, allowing in particular for processes with
infinite variation and a variety of dependencies between the underlying
processes. Multivariate classes developed by P\'erez-Abreu and Stelzer (2012)
and Semeraro (2008) and Guillaume (2013) are also submodels. The new models are
shown to be invariant under Esscher transforms, and quite explicit expressions
for canonical measures (and transition densities in some cases) are obtained,
which permit applications such as option pricing using PIDEs or tree based
methodologies. We illustrate with best-of and worst-of European and American
options on two assets.
