The shifted GARCH model with affine variance: Applications in pricing

This paper introduces a modification to the affine GARCH model of Heston and Nandi (2000). The new model is designed to allow for a non-zero lower bound for the variance achieved by adding two parameters to the existing model. The affine structure of the moment-generating function is preserved at the level of variance, while an approximation is studied for log prices. The construction resembles the shifted continuous-time Heston (1993) model. Maximum likelihood estimation is performed on real data, and the model is shown to improve the fitting of the implied volatility surface, particularly for deep out-of-the-money options. • We introduce a shifted affine GARCH model with a non-zero lower bound on variance. • The model fits US indices significantly better than the standard model. • The model allows for closed form (approximative) pricing of derivatives. • The fit to deep out-of-the-money put options is significantly improved.