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, la Heston and Nandi (2000). We compare the calibration performance on SPX options with the models of Heston and Nandi (2000), Christoffersen et al. (2006) and with a dynamic variance Gamma model introduced in Mercuri and Bellini (2011), obtaining promising results.