GARCH-M Model With an Asymmetric Risk Premium : Distinguishing Between ‘Good’ and ‘Bad’ Volatility Periods

We proposed the new method (GARCH-M-LEV) that allows capturing the asymmetry both 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 a 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. During most periods under consideration, we have found evidence of an asymmetric relationship between the risk premium and volatility changes. Due to this reason, the GARCH-M-LEV model usually was able to outperform the alternative GARCH family models according to the information criterion