Non-linear volatility with normal inverse Gaussian innovations: ad-hoc analytic option pricing

This paper proposes an approximate closed-form option-pricing model based on a non-linear GARCH process with Normal Inverse Gaussian (NIG) Lévy innovations. We develop the mathematical framework and demonstrate how to obtain a closed-form solution to the option price when the return dynamics are characterized by NIG innovations for volatility that follow a non-linear GARCH process. Using a sample of S&P 500 index options, we calibrate the proposed model alongside popular existing models. Overall, from a unified comparison of various analytic pricing approaches, we find that our model performs significantly better than existing models, both in-sample and out-of-sample.