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Modelling Regime-Specific Stock Price Volatility

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Author Info

  • Carol Alexander
  • Emese Lazar

Abstract

Single-state generalized autoregressive conditional heteroscedasticity (GARCH) models identify only one mechanism governing the response of volatility to market shocks, and the conditional higher moments are constant, unless modelled explicitly. So they neither capture state-dependent behaviour of volatility nor explain why the equity index skew persists into long-dated options. Markov switching (MS) GARCH models specify several volatility states with endogenous conditional skewness and kurtosis; of these the simplest to estimate is normal mixture (NM) GARCH, which has constant state probabilities. We introduce a state-dependent leverage effect to NM-GARCH and thereby explain the observed characteristics of equity index returns and implied volatility skews, without resorting to time-varying volatility risk premia. An empirical study on European equity indices identifies two-state asymmetric NM-GARCH as the best fit of the 15 models considered. During stable markets volatility behaviour is broadly similar across all indices, but the crash probability and the behaviour of returns and volatility during a crash depends on the index. The volatility mean-reversion and leverage effects during crash markets are quite different from those in the stable regime. Copyright (c) Blackwell Publishing Ltd and the Department of Economics, University of Oxford, 2009.

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Bibliographic Info

Article provided by Department of Economics, University of Oxford in its journal Oxford Bulletin of Economics and Statistics.

Volume (Year): 71 (2009)
Issue (Month): 6 (December)
Pages: 761-797

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Handle: RePEc:bla:obuest:v:71:y:2009:i:6:p:761-797

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Cited by:
  1. Massimo Guidolin & Stuart Hyde & David McMillan & Sadayuki Ono, 2010. "Does the macroeconomy predict U.K. asset returns in a nonlinear fashion? comprehensive out-of-sample evidence," Working Papers 2010-039, Federal Reserve Bank of St. Louis.
  2. Cifter, Atilla, 2012. "Volatility Forecasting with Asymmetric Normal Mixture Garch Model: Evidence from South Africa," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 127-142, June.
  3. Simon A. BRODA & Markus HAAS & Jochen KRAUSE & Marc S. PAOLELLA & Sven C. STEUDE, . "Stable Mixture GARCH Models," Swiss Finance Institute Research Paper Series 11-39, Swiss Finance Institute.
  4. Yin-Wong Cheung & Sang-Kuck Chung, 2011. "A Long Memory Model with Normal Mixture GARCH," Computational Economics, Society for Computational Economics, vol. 38(4), pages 517-539, November.
  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, vol. 26(C), pages 602-623.

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