GARCH-M model with an asymmetric risk premium: Distinguishing between ‘good’ and ‘bad’ volatility periods

Abstract

We proposed a new method (GARCH-M-GJR-LEV) that captures the asymmetry in the variance and return equations. The development of the model is encouraged by the stylized fact that investors demand a higher risk premium during “bad” volatility periods rather than “good” ones. To study the properties of the obtained estimators, we conducted simulated data analysis, considering a data-generating process characterized by asymmetric responses of risk premium to volatility changes. As a result, we have found statistical evidence in favor of a significant advantage of the proposed method compared to existing alternatives. Further, the proposed model was applied to study the S&P 500 market index. We have found evidence of an asymmetric relationship between the risk premium and volatility changes during most periods under consideration. Due to this, the GARCH-M-GJR-LEV model usually outperformed the alternative GARCH family models according to the information criteria.