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- McAleer, M.J. (2014): Asymmetry and Leverage in Conditional Volatility Models
__Abstract__ 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). ... These models are important in estimating and forecasting volatility, as well as capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and 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 two-fold, namely: (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; and (2) to show that leverage is not possible in these univariate conditional volatility models.
RePEc:ems:eureir:77759 Save to MyIDEAS - Michael McAleer (2014): Asymmetry and Leverage in Conditional Volatility Models
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). ... These models are important in estimating and forecasting volatility, as well as capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and 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 two-fold, namely: (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; and (2) to show that leverage is not possible in these univariate conditional volatility models.
RePEc:cbt:econwp:14/24 Save to MyIDEAS - Michael McAleer (2014): Asymmetry and Leverage in Conditional Volatility Models
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). ... 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.
RePEc:gam:jecnmx:v:2:y:2014:i:3:p:145-150:d:40585 Save to MyIDEAS - Michael McAleer (2014): Asymmetry and Leverage in Conditional Volatility Models
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). ... These models are important in estimating and forecasting volatility, as well as capturing asymmetry, which is the different effects on conditional volatility of positive and negative effects of equal magnitude, and 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 two-fold, namely: (1) to derive the GJR model from a random coefficient autoregressive process, with appropriate regularity conditions; and (2) to show that leverage is not possible in these univariate conditional volatility models.
RePEc:tin:wpaper:20140125 Save to MyIDEAS - Serge Darolles & Christian Francq & Gaëlle Le Fol & Jean-Michel Zakoïan (2016): Intrinsic Liquidity in Conditional Volatility Models
This paper aims at disentangling market risk and liquidity riskin the context of conditional volatility models.
RePEc:hal:journl:hal-01500747 Save to MyIDEAS - Serge Darolles & Gaëlle Le Fol & Christian Francq & Jean-Michel Zakoïan (2016): Intrinsic Liquidity in Conditional Volatility Models
This paper aims at disentangling market risk and liquidity risk in the context of conditional volatility models.
RePEc:adr:anecst:y:2016:i:123-124:p:225-245 Save to MyIDEAS - Harvey, Andrew (2010): Exponential conditional volatility models
The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score.
RePEc:cte:wsrepe:ws103620 Save to MyIDEAS - Harvey, A. (2010): Exponential Conditional Volatility Models
The asymptotic distribution of maximum likelihood estimators is derived for a class of exponential generalized autoregressive conditional heteroskedasticity (EGARCH) models. The result carries over to models for duration and realised volatility that use an exponential link function. A key feature of the model formulation is that the dynamics are driven by the score.
RePEc:cam:camdae:1040 Save to MyIDEAS - Asai, M. & McAleer, M.J. (2016): A Multivariate Asymmetric Long Memory Conditional Volatility Model with X, Regularity and Asymptotics
The paper derives a Multivariate Asymmetric Long Memory conditional volatility model with Exogenous Variables (X), or the MALMX model, with dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. ... The underlying vector random coefficient autoregressive process, which has well established regularity conditions and associated asymptotic properties, is discussed, and a simple explanation is given as to why only the diagonal BEKK model, and not the Hadamard, triangular or full BEKK models, has regularity conditions and asymptotic properties. Various special cases, including the diagonal BEKK model of Baba et al. (1985) and Engle and Kroner (1995), VARMA- GARCH model of Ling and McAleer (2003), and VARMA-AGARCH model of McAleer et al. (2009), are discussed. There does not seem to have been a derivation of a univariate conditional volatility model with exogenous variables (X) that has dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. Therefore, the derivation of a multivariate conditional volatility model with exogenous variables (X) that has regularity conditions and asymptotic theory would seem to be a significant extension of the existing literature.
RePEc:ems:eureir:93333 Save to MyIDEAS - Manabu Asai & Michael McAleer (2016): A Multivariate Asymmetric Long Memory Conditional Volatility Model with X, Regularity and Asymptotics
The paper derives a Multivariate Asymmetric Long Memory conditional volatility model with Exogenous Variables (X), or the MALMX model, with dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. ... The underlying vector random coefficient autoregressive process, which has well established regularity conditions and associated asymptotic properties, is discussed, and a simple explanation is given as to why only the diagonal BEKK model, and not the Hadamard, triangular or full BEKK models, has regularity conditions and asymptotic properties. Various special cases, including the diagonal BEKK model of Baba et al. (1985) and Engle and Kroner (1995), VARMA-GARCH model of Ling and McAleer (2003), and VARMA-AGARCH model of McAleer et al. (2009), are discussed. There does not seem to have been a derivation of a univariate conditional volatility model with exogenous variables (X) that has dynamic conditional correlations, appropriate regularity conditions, and associated asymptotic theory. Therefore, the derivation of a multivariate conditional volatility model with exogenous variables (X) that has regularity conditions and asymptotic theory would seem to be a significant extension of the existing literature.
RePEc:tin:wpaper:20160065 Save to MyIDEAS