Title: Two step modified-QML estimation for NIG-GARCH Processes
Authors: Christophe Chorro - University (France)
Fanirisoa Zazaravaka R Hasinavonizaka - Pantheon Sorbonne (France) [presenting]
Abstract: A two step Modified-Quasi Maximum likelihood (QML) procedure is proposed to estimate GARCH models with Normal Inverse Gaussian Distribution innovation (NIG). We provide also a comparison of GARCH-HN and GARCH-GJR models based on their capabilities of volatility modelling and forecasting abilities. Using our two step modified-QML estimation procedure, we model the volatility of S\&P500 using option-returns and VIX-returns and compare the performance of our model with Gaussian innovations. Our results suggest that improvements of the overall estimation are achieved when Modified-QML Estimation are used with VIX-returns and when NIG distribution is taken into account in the conditional variance. Moreover, it is found that NIG-GARCH-GJR allows better forecasts than Gaussian-GARCH-HN, Gaussian-GARCH-GJR and the NIG-GARCH-HN. Finally, increased performance of the forecasts is clearly observed when using non-normal distributions and numerical studies confirm the advantages of the proposed approach.