Volatility Modeling by Asymmetrical Quadratic Effect with Diminishing Marginal Impact

This study presents evidence of an asymmetrical quadratic effect from financial asset return on volatility. The relationships between the two variables are quadratic for both positive and negative returns and systematically different in the two regimes. The convex relations are observed showing that extreme shocks have a diminishing marginal impact on volatility. A threshold quadratic model under GARCH framework is developed to capture the effect and applied to major stock indices. The empirical outcomes of quadratic regressions and in-sample estimations significantly confirm the asymmetrical quadratic behavior. With application of S&P500 series, both diagnoses of in-sample estimations and evaluations of out-of-sample forecasts verify the proposed specification as a valid alternative volatility modeling.