Computational Economics

, Volume 37, Issue 3, pp 301–330 | Cite as

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.


Volatility modeling Quadratic Asymmetric Threshold GARCH 

JEL Classification

C22 C53 G10 G17 


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Copyright information

© Springer Science+Business Media, LLC. 2011

Authors and Affiliations

  1. 1.Department of FinanceYuan Ze UniversityChung-LiTaiwan

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