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

A First Option Calibration of the GARCH Diffusion Model by a PDE Method