Empirical and theoretical studies have attempted to establish the U-shape of the log-ratio of conditional risk-neutral and physical probability density functions. The main subject of this paper is to question the use of such a U-shaped pricing kernel to improve option pricing performances in a non-Gaussian setting. Starting from the so-called inverse Gaussian GARCH model (IG-GARCH), known to provide semi-closed-form formulas for classical European derivatives when an exponential-affine pricing kernel is used, we build a new pricing kernel that is non-monotonic and that still has this remarkable property. Using a daily dataset of call options written on the S&P500 index, we compare the pricing performances of these two IG-GARCH models proving, in this framework, that the new exponential U-shaped stochastic discount factor clearly outperforms the classical exponential-affine one. What is more, several estimation strategies including options or VIX information are evaluated taking advantage of the analytical tractability of these models. We prove that the parsimonious estimation approach using returns and VIX historical data remains competitive without having to work with the cross section of options.