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Cholesky realized stochastic volatility model

Author

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  • Shirota, Shinichiro
  • Omori, Yasuhiro
  • F. Lopes, Hedibert.
  • Piao, Haixiang
Abstract
Multivariate stochastic volatility models with leverage are expected to play important roles in financial applications such as asset allocation and risk management. However, these models suffer from two major difficulties: (1) there are too many parameters to estimate by using only daily asset returns and (2) estimated covariance matrices are not guaranteed to be positive definite. Our approach takes advantage of realized covariances to achieve the efficient estimation of parameters by incorporating additional information for the co-volatilities, and considers Cholesky decomposition to guarantee the positive definiteness of the covariance matrices. In this framework, a flexible model is proposed for stylized facts of financial markets, such as dynamic correlations and leverage effects among volatilities. By using the Bayesian approach, Markov Chain Monte Carlo implementation is described with a simple but efficient sampling scheme. Our model is applied to the data of nine U.S. stock returns, and it is compared with other models on the basis of portfolio performances.

Suggested Citation

  • Shirota, Shinichiro & Omori, Yasuhiro & F. Lopes, Hedibert. & Piao, Haixiang, 2017. "Cholesky realized stochastic volatility model," Econometrics and Statistics, Elsevier, vol. 3(C), pages 34-59.
    • Handle: RePEc:eee:ecosta:v:3:y:2017:i:c:p:34-59
    DOI: 10.1016/j.ecosta.2016.08.003
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    2. McCausland, William & Miller, Shirley & Pelletier, Denis, 2021. "Multivariate stochastic volatility using the HESSIAN method," Econometrics and Statistics, Elsevier, vol. 17(C), pages 76-94.
    3. Yuta Yamauchi & Yasuhiro Omori, 2020. "Dynamic factor, leverage and realized covariances in multivariate stochastic volatility," Papers 2011.06909, arXiv.org, revised Sep 2021.
    4. Yuta Yamauchi & Yasuhiro Omori, 2021. "Dynamic Factor, Leverage and Realized Covariances in Multivariate Stochastic Volatility," CIRJE F-Series CIRJE-F-1176, CIRJE, Faculty of Economics, University of Tokyo.
    5. Makoto Takahashi & Yuta Yamauchi & Toshiaki Watanabe & Yasuhiro Omori, 2024. "Realized Stochastic Volatility Model with Skew-t Distributions for Improved Volatility and Quantile Forecasting," Papers 2401.13179, arXiv.org, revised Oct 2024.
    6. Yuta Kurose & Yasuhiro Omori, "undated". "Multiple-lock Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1075, CIRJE, Faculty of Economics, University of Tokyo.
    7. Yuta Yamauchi & Yasuhiro Omori, 2018. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations," Papers 1809.09928, arXiv.org, revised Mar 2019.
    8. Gribisch, Bastian & Hartkopf, Jan Patrick, 2023. "Modeling realized covariance measures with heterogeneous liquidity: A generalized matrix-variate Wishart state-space model," Journal of Econometrics, Elsevier, vol. 235(1), pages 43-64.
    9. Yuta Yamauchi & Yasuhiro Omori, 2016. "Multivariate Stochastic Volatility Model with Realized Volatilities and Pairwise Realized Correlations ," CIRJE F-Series CIRJE-F-1029, CIRJE, Faculty of Economics, University of Tokyo.
    10. Mike West, 2020. "Bayesian forecasting of multivariate time series: scalability, structure uncertainty and decisions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 1-31, February.
    11. Yuta Kurose & Yasuhiro Omori, 2016. "Multiple-block Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1024, CIRJE, Faculty of Economics, University of Tokyo.
    12. Bruno P. C. Levy & Hedibert F. Lopes, 2021. "Dynamic Ordering Learning in Multivariate Forecasting," Papers 2101.04164, arXiv.org, revised Nov 2021.
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    14. Yuta Yamauchi & Yasuhiro Omori, 2020. "Dynamic Factor, Leverage and Realized Covariances in Multivariate Stochastic Volatility," CIRJE F-Series CIRJE-F-1158, CIRJE, Faculty of Economics, University of Tokyo.

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