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Asymmetric Multivariate Stochastic Volatility

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  • Manabu Asai
  • Michael McAleer

Abstract

This paper proposes and analyses two types of asymmetric multivariate stochastic volatility (SV) models, namely, (i) the SV with leverage (SV-L) model, which is based on the negative correlation between the innovations in the returns and volatility, and (ii) the 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, the Nikkei 225, and the 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 favor of their bivariate and trivariate counterparts.

Suggested Citation

  • Manabu Asai & Michael McAleer, 2006. "Asymmetric Multivariate Stochastic Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 453-473.
    • Handle: RePEc:taf:emetrv:v:25:y:2006:i:2-3:p:453-473
    DOI: 10.1080/07474930600712913
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