  Time-series calibrations often suggest that the GARCH diffusion model could
also be a suitable candidate for option (risk-neutral) calibration. But unlike
the popular Heston model, it lacks a fast, semi-analytic solution for the
pricing of vanilla options, perhaps the main reason why it is not used in this
way. In this paper we show how an efficient finite difference-based PDE solver
can effectively replace analytical solutions, enabling accurate option
calibrations in less than a minute. The proposed pricing engine is shown to be
robust under a wide range of model parameters and combines smoothly with
black-box optimizers. We use this approach to produce a first PDE calibration
of the GARCH diffusion model to SPX options and present some benchmark results
for future reference.
