We provide a novel stochastic volatility model based on the autoregressive Gamma process that allows for both a structure-preserving change to the risk-neutral measure and a non-Gaussian distribution for the return innovations. The model employs the Meixner distribution, which enriches the return dynamics with conditional stochastic skewness and kurtosis. We propose a fast and accurate estimation method by combining the approximate maximum likelihood method of Bates (2006). with a numerical integration technique suitable for highly oscillatory functions. We derive a closed-form discrete-time option pricing formula. The Meixner specification is superior to the benchmark of their family, especially when calibrated to option data