Description

In this paper we first derive an approximation of the moment generating function of the cumulative returns generated by the GARCH model proposed by Heston and Nandi (2000). Analytical cumulants align those presented in Mazzoni (2010), and numerical results support the quality of the approximation. Second, we provide a calibration that relates the parameters of the Heston–Nandi model with those of the Asymmetric GARCH (AGARCH) model. Although we acknowledge that both models are different, we find that variance and skewness behave similarly.