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Matrix exponential stochastic volatility with cross leverage

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  • Ishihara, Tsunehiro
  • Omori, Yasuhiro
  • Asai, Manabu

Abstract

A multivariate stochastic volatility model with the dynamic correlation and the cross leverage effect is described and its estimation using Markov chain Monte Carlo is proposed. The time-varying covariance matrices are guaranteed to be positive definite by using a matrix exponential transformation. Of particular interest is our approach for sampling a set of latent matrix logarithm variables from their conditional posterior distribution, where we construct the proposal density based on an approximating linear Gaussian state space model. The proposed model and its extensions with fat-tailed error distribution are applied to trivariate returns data (daily stocks, bonds, and exchange rates) of Japan. Further, a model comparison is conducted including constant correlation multivariate stochastic volatility models with leverage and diagonal multivariate GARCH models.

Suggested Citation

  • Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.
    • Handle: RePEc:eee:csdana:v:100:y:2016:i:c:p:331-350
    DOI: 10.1016/j.csda.2014.10.012
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    Cited by:

    1. Jouchi Nakajima & Tsuyoshi Kunihama & Yasuhiro Omori, 2017. "Bayesian modeling of dynamic extreme values: extension of generalized extreme value distributions with latent stochastic processes," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(7), pages 1248-1268, May.
    2. Ilya Archakov & Peter Reinhard Hansen & Asger Lunde, 2020. "A Multivariate Realized GARCH Model," Papers 2012.02708, arXiv.org, revised May 2024.
    3. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    4. Yuta Kurose, 2021. "Stochastic volatility model with range-based correction and leverage," Papers 2110.00039, arXiv.org, revised Oct 2021.
    5. Manabu Asai & Michael McAleer, 2022. "Bayesian Analysis of Realized Matrix-Exponential GARCH Models," Computational Economics, Springer;Society for Computational Economics, vol. 59(1), pages 103-123, January.
    6. Manabu Asai & Chia-Lin Chang & Michael McAleer, 2016. "Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers," Documentos de Trabajo del ICAE 2016-15, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    7. Kurose, Yuta & Omori, Yasuhiro, 2020. "Multiple-block dynamic equicorrelations with realized measures, leverage and endogeneity," Econometrics and Statistics, Elsevier, vol. 13(C), pages 46-68.
    8. 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.
    9. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.
    10. Jouchi Nakajima, 2017. "Bayesian analysis of multivariate stochastic volatility with skew return distribution," Econometric Reviews, Taylor & Francis Journals, vol. 36(5), pages 546-562, May.
    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. Kurose, Yuta & Omori, Yasuhiro, 2016. "Dynamic equicorrelation stochastic volatility," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 795-813.
    13. 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.
    14. Ilya Archakov & Peter Reinhard Hansen, 2021. "A New Parametrization of Correlation Matrices," Econometrica, Econometric Society, vol. 89(4), pages 1699-1715, July.
    15. Asai, Manabu & Chang, Chia-Lin & McAleer, Michael, 2022. "Realized matrix-exponential stochastic volatility with asymmetry, long memory and higher-moment spillovers," Journal of Econometrics, Elsevier, vol. 227(1), pages 285-304.
    16. Wu, Xinyu & Wang, Xiaona, 2020. "Forecasting volatility using realized stochastic volatility model with time-varying leverage effect," Finance Research Letters, Elsevier, vol. 34(C).
    17. Tian, Shuairu & Hamori, Shigeyuki, 2015. "Modeling interest rate volatility: A Realized GARCH approach," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 158-171.
    18. 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.

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