Abstracts

We unify and extend a number of approaches related to constructing multivariate Variance-Gamma (V.G.) models for the pricing of options on multiple assets. An overarching model is derived by subordinating multivariate Brownian motion to a subordinator from the Thorin (1977) class of generalised Gamma convolution subordinators. A special case is the well-known Madan-Seneta V.G. model, but our multivariate generalization is considerably wider, allowing in particular for processes with unbounded variation and a variety of dependencies between the underlying processes. Multivariate classes developed by Pérez-Abreu and Stelzer (2012) and Semeraro (2008) are also submodels.
We draw out some interesting connections in this respect. 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 option pricing using PIDEs or tree based methodologies. We illustrate with best-of and worst-of European and American options on two assets.