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Article

Asymmetry and Leverage in Conditional Volatility Models

by 1,2,3,4
1
Department of Quantitative Finance, National Tsing Hua University, Hsinchu 101, Taiwan
2
Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, Burgemeester Oudlaan 50, 3062 PA Rotterdam, The Netherlands
3
Tinbergen Institute, Rotterdam 3000 DR, The Netherlands
4
Department of Quantitative Economics, Complutense University of Madrid, Madrid, 28040, Spain 
Econometrics 2014, 2(3), 145-150; https://doi.org/10.3390/econometrics2030145
Received: 18 September 2014 / Revised: 19 September 2014 / Accepted: 19 September 2014 / Published: 24 September 2014
The three most popular univariate conditional volatility models are the generalized autoregressive conditional heteroskedasticity (GARCH) model of Engle (1982) and Bollerslev (1986), the GJR (or threshold GARCH) model of Glosten, Jagannathan and Runkle (1992), and the exponential GARCH (or EGARCH) model of Nelson (1990, 1991). The underlying stochastic specification to obtain GARCH was demonstrated by Tsay (1987), and that of EGARCH was shown recently in McAleer and Hafner (2014). These models are important in estimating and forecasting volatility, as well as in capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and purportedly in capturing leverage, which is the negative correlation between returns shocks and subsequent shocks to volatility. As there seems to be some confusion in the literature between asymmetry and leverage, as well as which asymmetric models are purported to be able to capture leverage, the purpose of the paper is three-fold, namely, (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; (2) to show that leverage is not possible in the GJR and EGARCH models; and (3) to present the interpretation of the parameters of the three popular univariate conditional volatility models in a unified manner. View Full-Text
Keywords: conditional volatility models; random coefficient autoregressive processes; random coefficient complex nonlinear moving average process; asymmetry; leverage conditional volatility models; random coefficient autoregressive processes; random coefficient complex nonlinear moving average process; asymmetry; leverage
MDPI and ACS Style

McAleer, M. Asymmetry and Leverage in Conditional Volatility Models. Econometrics 2014, 2, 145-150. https://doi.org/10.3390/econometrics2030145

AMA Style

McAleer M. Asymmetry and Leverage in Conditional Volatility Models. Econometrics. 2014; 2(3):145-150. https://doi.org/10.3390/econometrics2030145

Chicago/Turabian Style

McAleer, Michael. 2014. "Asymmetry and Leverage in Conditional Volatility Models" Econometrics 2, no. 3: 145-150. https://doi.org/10.3390/econometrics2030145

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