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Asymmetric Multivariate Stochastic Volatility

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Author Info
Manabu Asai
Michael McAleer

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Abstract

This paper proposes and analyses two types of asymmetric multivariate stochastic volatility (SV) models, namely: (i) SV with leverage (SV-L) model, which is based on the negative correlation between the innovations in the returns and volatility; and (ii) SV with leverage and size effect (SV-LSE) model, which is based on the signs and magnitude of the returns. The paper derives the state space form for the logarithm of the squared returns which follow the multivariate SV-L model, and develops estimation methods for the multivariate SV-L and SV-LSE models based on the Monte Carlo likelihood (MCL) approach. The empirical results show that the multivariate SV-LSE model fits the bivariate and trivariate returns of the S&P 500, Nikkei 225, and Hang Seng indexes with respect to AIC and BIC more accurately than does the multivariate SV-L model. Moreover, the empirical results suggest that the univariate models should be rejected in favour of their bivariate and trivariate counterparts.

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Paper provided by Universitat de les Illes Balears, Departament d'Economía Aplicada in its series DEA Working Papers with number 12.

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Date of creation: Nov 2005
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Handle: RePEc:ubi:deawps:12

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Related research
Keywords: Multivariate stochastic volatility; asymmetric leverage; dynamic leverage; size effect; numerical likelihood; Bayesian Markov chain Monte Carlo; importance sampling.;

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  3. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September. [Downloadable!] (restricted)
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  22. Danielsson, Jon, 1994. "Stochastic volatility in asset prices estimation with simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 375-400. [Downloadable!] (restricted)
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    Other versions:
  25. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
    Other versions:
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Cited by:
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  1. Fulvia Focker & Umberto Triacca, 2006. "A new proxy of the average volatility of a basket of returns: A Monte Carlo study," Economics Bulletin, Economics Bulletin, vol. 3(15), pages 1-14. [Downloadable!]
  2. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility," CIRJE F-Series CIRJE-F-488, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
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