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Alternative Asymmetric Stochastic Volatility Models

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  • Asai, M.
  • McAleer, M.J.

Abstract

The stochastic volatility model usually incorporates asymmetric effects by introducing the negative correlation between the innovations in returns and volatility. In this paper, we propose a new asymmetric stochastic volatility model, based on the leverage and size effects. The model is a generalization of the exponential GARCH (EGARCH) model of Nelson (1991). We consider categories for asymmetric effects, which describes the difference among the asymmetric effect of the EGARCH model, the threshold effects indicator function of Glosten, Jagannathan and Runkle (1992), and the negative correlation between the innovations in returns and volatility. The new model is estimated by the efficient importance sampling method of Liesenfeld and Richard (2003), and the finite sample properties of the estimator are investigated using numerical simulations. Four financial time series are used to estimate the alternative asymmetric SV models, with empirical asymmetric effects found to be statistically significant in each case. The empirical results for S&P 500 and Yen/USD returns indicate that the leverage and size effects are significant, supporting the general model. For TOPIX and USD/AUD returns, the size effect is insignificant, favoring the negative correlation between the innovations in returns and volatility. We also consider standardized t distribution for capturing the tail behavior. The results for Yen/USD returns show that the model is correctly specified, while the results for three other data sets suggest there is scope for improvement.

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Bibliographic Info

Paper provided by Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute in its series Econometric Institute Research Papers with number EI 2010-69.

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Date of creation: 07 Dec 2010
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Handle: RePEc:ems:eureir:21730

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Keywords: asymmetric effects; importance sampling; indicator function; leverage; numerical simulations; stochastic volatility; threshold;

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Citations

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Cited by:
  1. Afonso, António & Gomes, Pedro & Taamouti, Abderrahim, 2014. "Sovereign credit ratings, market volatility, and financial gains," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 20-33.
  2. Michael McAleer, 2009. "The Ten Commandments for Optimizing Value-at-Risk and Daily Capital Charges," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-652, CIRJE, Faculty of Economics, University of Tokyo.
  3. Bretó, Carles, 2014. "On idiosyncratic stochasticity of financial leverage effects," Statistics & Probability Letters, Elsevier, Elsevier, vol. 91(C), pages 20-26.
  4. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2011. "Asymmetry and Long Memory in Volatility Modelling," Documentos de Trabajo del ICAE, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico 2011-29, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
  5. Carles Bret\'o, 2013. "On idiosyncratic stochasticity of financial leverage effects," Papers 1312.5496, arXiv.org.
  6. Manabu Asai & Michael McAleer & Marcelo C. Medeiros, 2009. "Asymmetry and Leverage in Realized Volatility," CIRJE F-Series, CIRJE, Faculty of Economics, University of Tokyo CIRJE-F-656, CIRJE, Faculty of Economics, University of Tokyo.
  7. Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Time-varying mixture GARCH models and asymmetric volatility," The North American Journal of Economics and Finance, Elsevier, Elsevier, vol. 26(C), pages 602-623.
  8. Xiuping Mao & Esther Ruiz & Helena Veiga, 2013. "One for all : nesting asymmetric stochastic volatility models," Statistics and Econometrics Working Papers, Universidad Carlos III, Departamento de Estadística y Econometría ws131110, Universidad Carlos III, Departamento de Estadística y Econometría.
  9. Wang, Joanna J.J., 2012. "On asymmetric generalised t stochastic volatility models," Mathematics and Computers in Simulation (MATCOM), Elsevier, Elsevier, vol. 82(11), pages 2079-2095.

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