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Alternative Asymmetric Stochastic Volatility Models

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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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File URL: http://www.econ.canterbury.ac.nz/RePEc/cbt/econwp/1070.pdf
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Bibliographic Info

Paper provided by University of Canterbury, Department of Economics and Finance in its series Working Papers in Economics with number 10/70.

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Length: 26 pages
Date of creation: 01 Nov 2010
Date of revision:
Handle: RePEc:cbt:econwp:10/70

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

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Citations

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Cited by:
  1. Michael McAleer, 2009. "The Ten Commandments For Optimizing Value-At-Risk And Daily Capital Charges," Journal of Economic Surveys, Wiley Blackwell, Wiley Blackwell, vol. 23(5), pages 831-849, December.
  2. Carles Bret\'o, 2013. "On idiosyncratic stochasticity of financial leverage effects," Papers 1312.5496, arXiv.org.
  3. Asai, M. & McAleer, M.J. & Medeiros, M.C., 2008. "Asymmetry and leverage in realized volatility," Econometric Institute Research Papers EI 2008-31, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  4. 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.
  5. 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.
  6. Bretó, Carles, 2014. "On idiosyncratic stochasticity of financial leverage effects," Statistics & Probability Letters, Elsevier, Elsevier, vol. 91(C), pages 20-26.
  7. Asai, M. & McAleer, M.J. & Medeiros, M.C., 2010. "Asymmetry and Long Memory in Volatility Modelling," Econometric Institute Research Papers EI 2010-60, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  8. 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.
  9. António Afonso & Pedro Gomes & Abderrahim Taamouti, 2014. "Sovereign credit ratings, market volatility, and financial gains," Working Papers Department of Economics, ISEG - School of Economics and Management, Department of Economics, University of Lisbon 2014/06, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.

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