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Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors

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Author Info

  • Tsunehiro Ishihara

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

Abstract

The efficient Bayesian estimation method using Markov chain Monte Carlo is proposed for a multivariate stochastic volatility model that is a natural extension of the univariate stochastic volatility model with leverage and heavy-tailed errors, where we further incorporate cross leverage effects among stock returns. Our method is based on a multi-move sampler which samples a block of latent volatility vectors and is described first in the literature for a multivariate stochastic volatility model with cross leverage and heavy-tailed errors. Its high sampling efficiency is shown using numerical examples in comparison with a single-move sampler which samples one latent volatility vector at a time given other latent vectors and parameters. The empirical studies are given using five dimensional stock return indices in Tokyo Stock Exchange.

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File URL: http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/206.pdf
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Bibliographic Info

Paper provided by Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-198.

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Length: 29 pages
Date of creation: Dec 2009
Date of revision:
Handle: RePEc:cfi:fseres:cf198

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References

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  1. Jouchi Nakajima & Yasuhiro Omori, 2009. "Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student's t-Distribution," CIRJE F-Series CIRJE-F-701, CIRJE, Faculty of Economics, University of Tokyo.
  2. Neil Shephard & Siddhartha Chib, 1999. "Analysis of High Dimensional Multivariate Stochastic Volatility Models," Economics Series Working Papers 1999-W18, University of Oxford, Department of Economics.
  3. Manabu Asai & Michael McAleer, 2005. "Asymmetric Multivariate Stochastic Volatility," DEA Working Papers 12, Universitat de les Illes Balears, Departament d'Economía Aplicada.
  4. Tsunehiro Ishihara & Yasuhiro Omori, 2009. "Multivariate Stochastic Volatility with Cross Leverage," CARF F-Series CARF-F-191, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  5. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
  6. Eric Jacquier & Nicholas G. Polson & Peter Rossi, . "Stochastic Volatility: Univariate and Multivariate Extensions," Rodney L. White Center for Financial Research Working Papers 19-95, Wharton School Rodney L. White Center for Financial Research.
  7. Asai, M. & Caporin, M., 2009. "Block Structure Multivariate Stochastic Volatility Models," Econometric Institute Research Papers EI 2009-51, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  8. Jun Yu & Renate Meyer, 2004. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Working Papers 23-2004, Singapore Management University, School of Economics.
  9. Omori, Yasuhiro & Watanabe, Toshiaki, 2008. "Block sampler and posterior mode estimation for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2892-2910, February.
  10. Carmen Broto & Esther Ruiz, 2004. "Estimation methods for stochastic volatility models: a survey," Journal of Economic Surveys, Wiley Blackwell, vol. 18(5), pages 613-649, December.
  11. David Chan & Robert Kohn & Chris Kirby, 2006. "Multivariate Stochastic Volatility Models with Correlated Errors," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 245-274.
  12. Nakajima, Jouchi & Omori, Yasuhiro, 2009. "Leverage, heavy-tails and correlated jumps in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2335-2353, April.
  13. Harvey, Andrew & Ruiz, Esther & Shephard, Neil, 1994. "Multivariate Stochastic Variance Models," Review of Economic Studies, Wiley Blackwell, vol. 61(2), pages 247-64, April.
  14. Takahashi, Makoto & Omori, Yasuhiro & Watanabe, Toshiaki, 2009. "Estimating stochastic volatility models using daily returns and realized volatility simultaneously," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2404-2426, April.
  15. Toshiaki Watanabe, 2004. "A multi-move sampler for estimating non-Gaussian time series models: Comments on Shephard & Pitt (1997)," Biometrika, Biometrika Trust, vol. 91(1), pages 246-248, March.
  16. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649 Elsevier.
  17. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
  18. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
  19. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
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Cited by:
  1. Jouchi Nakajima & Yasuhiro Omori, 2010. "Stochastic Volatility Model with Leverage and Asymmetrically Heavy-Tailed Error Using GH Skew Student?s t-Distribution," CARF F-Series CARF-F-215, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  2. António Alberto Santos & João Andrade, 2014. "Stochastic Volatility Estimation with GPU Computing," GEMF Working Papers 2014-10, GEMF - Faculdade de Economia, Universidade de Coimbra.
  3. Yuta Kurose & Yasuhiro Omori, 2013. "Dynamic Equicorrelation Stochastic Volatility," CIRJE F-Series CIRJE-F-907, CIRJE, Faculty of Economics, University of Tokyo.

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