A Non-Gaussian, Structure-Preserving Stochastic Volatility and Option Pricing Model in Discrete Time

We propose a novel stochastic volatility model based on the autoregressive gamma process that accommodates a structure-preserving change to the risk-neutral measure while relying on a non-Gaussian distribution for the return innovations. The model employs the Meixner (MXN) 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 David S. Bates with a numerical integration technique suitable for highly oscillatory functions. We derive a closed-form discrete-time option pricing formula. The MXN model performs particularly well, compared to benchmarks within its class and of the generalized autoregressive conditional heteroskedasticity family, when calibrated directly to option data and when applied to option data with a high level of implied volatility, such as Bitcoin.