Option pricing in a conditional bilateral gamma model

We propose a conditional Bilateral Gamma model, in which the shape parameters of the Bilateral Gamma distribution have a Garch-like dynamics. After risk neutralization by means of a Bilateral Esscher Transform, the model admits a recursive procedure for the computation of the characteristic function of the underlying at maturity, à la Heston and Nandi (2000). We compare the calibration performance on SPX options with the models of Heston and Nandi (2000), Christoffersen, Heston and Jacobs (2006) and with a Dynamic Variance Gamma model introduced in Mercuri and Bellini (2011), obtaining promising results