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Multivariate Stochastic Volatility with Cross Leverage

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Author Info

  • Tsunehiro Ishihara

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

Abstract

We describe and estimate for the first time a natural multivariate extension of the univariate stochastic volatility model with leverage. The model, which we call the multivariate stochastic volatility with cross leverage, is fit by a tuned Bayesian MCMC method. Of particular general interest is our approach for sampling the state variables from the posterior distribution conditioned on the parameters. The state variables are sampled in blocks by the Metropolis-Hastings algorithm in which the proposal density is derived from an approximating linear Gaussian state space model. The conditional modes of the latent volatility variables are computed using a method of scoring where the covariance matrix of the proposal density is guaranteed to be positive definite. The auxiliary particle filter to compute the likelihood function is also shown and the model and the techniques are illustrated with daily stock returns data from the Tokyo Stock Exchange.

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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-690.

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Length: 19pages
Date of creation: Nov 2009
Date of revision:
Handle: RePEc:tky:fseres:2009cf690

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Cited by:
  1. Caporin, M. & McAleer, M.J., 2012. "Robust Ranking of Multivariate GARCH Models by Problem Dimension," Econometric Institute Research Papers EI2012-13, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  2. Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," "Marco Fanno" Working Papers 0124, Dipartimento di Scienze Economiche "Marco Fanno".
  3. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 56(11), pages 3674-3689.
  4. Geert Mesters & Bernd Schwaab & Siem Jan Koopman, 2014. "A Dynamic Yield Curve Model with Stochastic Volatility and Non-Gaussian Interactions: An Empirical Study of Non-standard Monetary Policy in the Euro Area," Tinbergen Institute Discussion Papers 14-071/III, Tinbergen Institute.
  5. Trojan, Sebastian, 2014. "Multivariate Stochastic Volatility with Dynamic Cross Leverage," Economics Working Paper Series 1424, University of St. Gallen, School of Economics and Political Science.
  6. Caporin, Massimiliano, 2013. "Equity and CDS sector indices: Dynamic models and risk hedging," The North American Journal of Economics and Finance, Elsevier, vol. 25(C), pages 261-275.
  7. Skaug, Hans J. & Yu, Jun, 2014. "A flexible and automated likelihood based framework for inference in stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 642-654.
  8. Santos, André A.P. & Moura, Guilherme V., 2014. "Dynamic factor multivariate GARCH model," Computational Statistics & Data Analysis, Elsevier, Elsevier, vol. 76(C), pages 606-617.

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