Towards a Delta-Gamma Sato Multivariate Model

In this paper, we propose a multivariate Lévy model as an extension of the univariate Difference of Gammas model introduced by Finlay and Seneta. The construction is based on the work of Mathai and Moschopoulos, where we model the log price gains and losses by separate Gamma processes, each containing a common and idiosyncratic components. Furthermore, we extend this multivariate model to the Sato setting, allowing for a better replication of the univariate option prices in both the strike and time-to-maturity dimensions. A numerical study reveals the advantages of these new types of multivariate models, compared to a multivariate VG model