  We present a discrete time stochastic volatility model in which the
conditional distribution of the logreturns is a Variance-Gamma, that is a
normal variance-mean mixture with Gamma mixing density. We assume that the
Gamma mixing density is time varying and follows an affine Garch model, trying
to capture persistence of volatility shocks and also higher order conditional
dynamics in a parsimonious way. We select an equivalent martingale measure by
means of the conditional Esscher transform as in Buhlmann et al. (1996) and
show that this change of measure leads to a similar dynamics of the mixing
distribution. The model admits a recursive procedure for the computation of the
characteristic function of the terminal logprice, thus allowing semianalytical
pricing as in Heston and Nandi (2000). From an empirical point of view, we
check the ability of this model to calibrate SPX option data and we compare it
with the Heston and Nandi (2000) model and with the Christoffersen, Heston and
Jacobs (2006) model, that is based on Inverse Gaussian innovations. Moreover,
we provide a detailed comparison with several variants of the Heston and Nandi
model that shows the superiority of the Variance-Gamma innovations also from
the point of view of historical MLE estimation.
