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Matrix Exponential Stochastic Volatility with Cross Leverage

Author

Listed:
  • Tsunehiro Ishihara

    (Graduate School of Economics, University of Tokyo)

  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

  • Manabu Asai

    (Faculty of Economics, Soka University)

Abstract

A multivariate stochastic volatility model with dynamic correlation and leverage effect is described and estimated. The matrix exponential transformation is used to keep the time-varying covariance matrices positive definite. An efficient Bayesian estimation method using Markov chain Monte Carlo is proposed. Of particular interest is our approach for sampling the latent state variables from the conditional posterior distribution, using a blocked multi-move Metropolis-Hastings sampling, in which the proposal density is derived from an approximating linear Gaussian state space model. The proposed model is applied to the daily stock price index, the Japanese bond price index, and the Yen/USD exchange rate returns data.

Suggested Citation

  • Tsunehiro Ishihara & Yasuhiro Omori & Manabu Asai, 2011. "Matrix Exponential Stochastic Volatility with Cross Leverage," CIRJE F-Series CIRJE-F-812, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2011cf812
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    Citations

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    Cited by:

    1. Yuta Kurose, 2021. "Stochastic volatility model with range-based correction and leverage," Papers 2110.00039, arXiv.org, revised Oct 2021.
    2. Chen, Han & Fei, Yijie & Yu, Jun, 2025. "Multivariate stochastic volatility models based on generalized Fisher transformation," Journal of Econometrics, Elsevier, vol. 251(C).
    3. 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.
    4. 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.
    5. 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.
    6. Ilya Archakov & Peter Reinhard Hansen, 2021. "A New Parametrization of Correlation Matrices," Econometrica, Econometric Society, vol. 89(4), pages 1699-1715, July.
    7. Khoo, Zhi De & Ng, Kok Haur & Koh, You Beng & Ng, Kooi Huat, 2025. "Forecasting financial volatility: An approach based on Parkinson volatility measure with long memory stochastic range model," Journal of Empirical Finance, Elsevier, vol. 82(C).
    8. 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.
    9. Ilya Archakov & Peter Reinhard Hansen & Asger Lunde, 2020. "A Multivariate Realized GARCH Model," Papers 2012.02708, arXiv.org, revised Feb 2025.
    10. 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.
    11. Kurose, Yuta & Omori, Yasuhiro, 2016. "Dynamic equicorrelation stochastic volatility," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 795-813.
    12. Asai, M. & Chang, C-L. & McAleer, M.J., 2016. "Realized Matrix-Exponential Stochastic Volatility with Asymmetry, Long Memory and Spillovers," Econometric Institute Research Papers EI2016-41, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. 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.
    14. 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.
    15. Wu, Xinyu & Wang, Xiaona, 2020. "Forecasting volatility using realized stochastic volatility model with time-varying leverage effect," Finance Research Letters, Elsevier, vol. 34(C).
    16. Yuta Kurose & Yasuhiro Omori, 2016. "Multiple-block Dynamic Equicorrelations with Realized Measures, Leverage and Endogeneity," CIRJE F-Series CIRJE-F-1022, CIRJE, Faculty of Economics, University of Tokyo.
    17. 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.
    18. Ewa Feder-Sempach & Piotr Szczepocki & Joanna Bogołębska, 2024. "Global uncertainty and potential shelters: gold, bitcoin, and currencies as weak and strong safe havens for main world stock markets," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 10(1), pages 1-23, December.
    19. 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.
    20. Tian, Shuairu & Hamori, Shigeyuki, 2015. "Modeling interest rate volatility: A Realized GARCH approach," Journal of Banking & Finance, Elsevier, vol. 61(C), pages 158-171.
    21. 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.

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