TianyiWang HongYan ZhuoHuang
This paper develops a new approach with realized higher moments to model the time varying distribution of ﬁnancial returns. Based on Gram-Charlier expansion(GCE) density, we explicitly link the expansion parameters with moments that are calculated based on intraday returns using an extended Realized GARCH frame work. The Cornish-Fish erexpansion is the napplied to forecast Value-at-Risk (VaR) with estimated moments to demonstrate the economic significance of the new model. Compared with the daily return based dynamic higher moments models, the inclusion of realized higher moments can significantly improve the model’s ability to forecast extreme tails. Our empirical results indicate that the new model significantly out performs traditional models in terms of the extreme VaR forecasting. In addition, we provide a formula to correct the moments associated with the commonly used squared transformation of GCE. Our empirical evidence also high lights the importance of using the correct moments over the original skewness and kurtosis parameter for GCE in VaR forecast.
Keywords: Realized higher moments, Realized GARCH, Gram-Charlier expansion, Value-at-Risk
JEL classiﬁcation: C22,C52,C58,Q47