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Realized GARCH: A Complete Model of Returns and Realized Measures of Volatility

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  • Peter Reinhard Hansen

    ()
    (Stanford University)

  • Zhuo (Albert) Huang

    (Stanford University)

  • Howard Howan Shek

    (Stanford University)

Abstract

GARCH models have been successful in modeling financial returns. Still, much is to be gained by incorporating a realized measure of volatility in these models. In this paper we introduce a new framework for the joint modeling of returns and realized measures of volatility. The Realized GARCH framework nests most GARCH models as special cases and is, in many ways, a natural extension of standard GARCH models. We pay special attention to linear and log-linear Realized GARCH specifications. This class of models has several attractive features. It retains the simplicity and tractability of the classical GARCH framework; it implies an ARMA structure for the conditional variance and realized measures of volatility; and models in this class are parsimonious and simple to estimate. A key feature of the Realized GARCH framework is a measurement equation that relates the observed realized measure to latent volatility. This equation facilitates a simple modeling of the dependence between returns and future volatility that is commonly referred to as the leverage effect. An empirical application with DJIA stocks and an exchange traded index fund shows that a simple Realized GARCH structure leads to substantial improvements in the empirical fit over to the standard GARCH model. This is true in-sample as well as out-of-sample. Moreover, the point estimates are remarkably similar across the different time series.

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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-13.

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Length: 46
Date of creation:
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Handle: RePEc:aah:create:2010-13

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Web page: http://www.econ.au.dk/afn/

Related research

Keywords: GARCH; High Frequency Data; Realized Variance; Leverage Effect;

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References

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Citations

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Cited by:
  1. Jozef Barunik & Lukas Vacha, 2012. "Modeling and forecasting exchange rate volatility in time-frequency domain," Papers 1204.1452, arXiv.org, revised Aug 2013.
  2. Jun Yu, 2008. "A Semiparametric Stochastic Volatility Model," Working Papers, Sim Kee Boon Institute for Financial Economics CoFie-04-2008, Sim Kee Boon Institute for Financial Economics.
  3. Roxana Halbleib & Valerie Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Papers ECARES, ULB -- Universite Libre de Bruxelles ECARES 2010-002, ULB -- Universite Libre de Bruxelles.
  4. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2011. "Financial Risk Measurement for Financial Risk Management," CREATES Research Papers, School of Economics and Management, University of Aarhus 2011-37, School of Economics and Management, University of Aarhus.
  5. Siem Jan Koopman & Marcel Scharth, 2012. "The Analysis of Stochastic Volatility in the Presence of Daily Realized Measures," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(1), pages 76-115, December.
  6. Dimitrios P. Louzis & Spyros Xanthopoulos‐Sisinis & Apostolos P. Refenes, 2013. "The Role of High‐Frequency Intra‐daily Data, Daily Range and Implied Volatility in Multi‐period Value‐at‐Risk Forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., John Wiley & Sons, Ltd., vol. 32(6), pages 561-576, 09.
  7. Heejoon Han & Dennis Kristensen, 2012. "Asymptotic Theory for the QMLE in GARCH-X Models with Stationary and Non-Stationary Covariates," CREATES Research Papers, School of Economics and Management, University of Aarhus 2012-25, School of Economics and Management, University of Aarhus.
  8. Giampiero M. Gallo & Edoardo Otranto, 2012. "Realized Volatility and Change of Regimes," Econometrics Working Papers Archive, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti" 2012_02, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti", revised Jul 2012.
  9. Masato Ubukata & Toshiaki Watanabe, 2011. "Pricing Nikkei 225 Options Using Realized Volatility," IMES Discussion Paper Series, Institute for Monetary and Economic Studies, Bank of Japan 11-E-18, Institute for Monetary and Economic Studies, Bank of Japan.
  10. Beare, Brendan K. & Schmidt, Lawrence, 2011. "An Empirical Test of Pricing Kernel Monotonicity," University of California at San Diego, Economics Working Paper Series, Department of Economics, UC San Diego qt5572n8pc, Department of Economics, UC San Diego.
  11. Matthias R. Fengler & Ostap Okhrin, 2012. "Realized Copula," SFB 649 Discussion Papers, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany SFB649DP2012-034, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  12. Manabu Asai & Michael McAleer, 2014. "Forecasting Co-Volatilities via Factor Models with Asymmetry and Long Memory in Realized Covariance," Working Papers in Economics, University of Canterbury, Department of Economics and Finance 14/10, University of Canterbury, Department of Economics and Finance.
  13. Çelik, Sibel & Ergin, Hüseyin, 2014. "Volatility forecasting using high frequency data: Evidence from stock markets," Economic Modelling, Elsevier, Elsevier, vol. 36(C), pages 176-190.
  14. Pierre Chausse & Dinghai Xu, 2012. "GMM Estimation of a Stochastic Volatility Model with Realized Volatility: A Monte Carlo Study," Working Papers, University of Waterloo, Department of Economics 1203, University of Waterloo, Department of Economics, revised May 2012.

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