[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
IDEAS home Printed from https://ideas.repec.org/p/tky/fseres/2014cf938.html
   My bibliography  Save this paper

Matrix Exponential Stochastic Volatility with Cross Leverage

Author

Listed:
  • Tsunehiro Ishihara

    (Department of Economics, Hitotsubashi University)

  • Yasuhiro Omori

    (Faculty of Economics, The University of Tokyo)

  • Manabu Asai

    (Faculty of Economics, Soka University)

Abstract
A multivariate stochastic volatility model with the dynamic correlation and the cross leverage effect is described and its efficient estimation method 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 extended models 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

  • Tsunehiro Ishihara & Yasuhiro Omori & Manabu Asai, 2014. "Matrix Exponential Stochastic Volatility with Cross Leverage," CIRJE F-Series CIRJE-F-938, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2014cf938
    as

    Download full text from publisher

    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2014/2014cf938.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Antonietta Mira, 2001. "On Metropolis-Hastings algorithms with delayed rejection," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3-4), pages 231-241.
    2. Chib, Siddhartha, 2001. "Markov chain Monte Carlo methods: computation and inference," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 57, pages 3569-3649, Elsevier.
    3. Manabu Asai & Michael McAleer, 2006. "Asymmetric Multivariate Stochastic Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 453-473.
    4. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    6. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3674-3689.
    7. Loddo, Antonello & Ni, Shawn & Sun, Dongchu, 2011. "Selection of Multivariate Stochastic Volatility Models via Bayesian Stochastic Search," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 342-355.
    8. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 145-175.
    9. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
    10. Ole E. Barndorff-Nielsen & Neil Shephard, 2004. "Econometric Analysis of Realized Covariation: High Frequency Based Covariance, Regression, and Correlation in Financial Economics," Econometrica, Econometric Society, vol. 72(3), pages 885-925, May.
    11. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    12. Audrino, Francesco & Corsi, Fulvio, 2010. "Modeling tick-by-tick realized correlations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2372-2382, November.
    13. Xin Jin & John M. Maheu, 2013. "Modeling Realized Covariances and Returns," Journal of Financial Econometrics, Oxford University Press, vol. 11(2), pages 335-369, March.
    14. Borus Jungbacker & Siem Jan Koopman, 2006. "Monte Carlo Likelihood Estimation for Three Multivariate Stochastic Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 385-408.
    15. Yasuhiro Omori & Siddhartha Chib & Neil Shephard & Jouchi Nakajima, 2004. "Stochastic volatility with leverage: fast likelihood inference," Economics Papers 2004-W19, Economics Group, Nuffield College, University of Oxford.
    16. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.
    17. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, vol. 134(1), pages 95-128, September.
    18. 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.
    19. Abadir,Karim M. & Magnus,Jan R., 2005. "Matrix Algebra," Cambridge Books, Cambridge University Press, number 9780521537469, September.
    20. LeSage, James P. & Kelley Pace, R., 2007. "A matrix exponential spatial specification," Journal of Econometrics, Elsevier, vol. 140(1), pages 190-214, September.
    21. Diaa Noureldin & Neil Shephard & Kevin Sheppard, 2012. "Multivariate high‐frequency‐based volatility (HEAVY) models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 907-933, September.
    22. David J. Spiegelhalter & Nicola G. Best & Bradley P. Carlin & Angelika Van Der Linde, 2002. "Bayesian measures of model complexity and fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(4), pages 583-639, October.
    23. Golosnoy, Vasyl & Gribisch, Bastian & Liesenfeld, Roman, 2012. "The conditional autoregressive Wishart model for multivariate stock market volatility," Journal of Econometrics, Elsevier, vol. 167(1), pages 211-223.
    24. Jun Yu & Renate Meyer, 2006. "Multivariate Stochastic Volatility Models: Bayesian Estimation and Model Comparison," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 361-384.
    25. Jan R. Magnus & Karim M. Abadir, 2007. "On some definitions in matrix algebra," CIRJE F-Series CIRJE-F-476, CIRJE, Faculty of Economics, University of Tokyo.
    26. Omori, Yasuhiro & Watanabe, Toshiaki, 2008. "Block sampler and posterior mode estimation for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2892-2910, February.
    27. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    28. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    29. Gourieroux, C. & Jasiak, J. & Sufana, R., 2009. "The Wishart Autoregressive process of multivariate stochastic volatility," Journal of Econometrics, Elsevier, vol. 150(2), pages 167-181, June.
    30. Manabu Asai & Michael McAleer, 2009. "Multivariate stochastic volatility, leverage and news impact surfaces," Econometrics Journal, Royal Economic Society, vol. 12(2), pages 292-309, July.
    31. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    32. Asai, M. & Caporin, M., 2009. "Block Structure Multivariate Stochastic Volatility Models," Econometric Institute Research Papers EI 2009-51, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    33. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    34. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    35. Toshiaki Watanabe, 2004. "A multi-move sampler for estimating non-Gaussian time series models: Comments on Shephard & Pitt (1997)," Biometrika, Biometrika Trust, vol. 91(1), pages 246-248, March.
    36. Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," The Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-844.
    37. Tsunehiro Ishihara & Yasuhiro Omori, 2009. "Multivariate Stochastic Volatility with Cross Leverage," CARF F-Series CARF-F-191, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    38. David Chan & Robert Kohn & Chris Kirby, 2006. "Multivariate Stochastic Volatility Models with Correlated Errors," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 245-274.
    39. Philipov, Alexander & Glickman, Mark E., 2006. "Multivariate Stochastic Volatility via Wishart Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 313-328, July.
    40. Alexander Philipov & Mark Glickman, 2006. "Factor Multivariate Stochastic Volatility via Wishart Processes," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 311-334.
    41. Luc Bauwens & David Veredas & Winfried Pohlmeier, 2005. "High frequency finance," ULB Institutional Repository 2013/136220, ULB -- Universite Libre de Bruxelles.
    42. repec:cup:cbooks:9780521822893 is not listed on IDEAS
    43. Gregory Bauer & Keith Vorkink, 2007. "Multivariate Realized Stock Market Volatility," Staff Working Papers 07-20, Bank of Canada.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Kurose, Yuta & Omori, Yasuhiro, 2016. "Dynamic equicorrelation stochastic volatility," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 795-813.
    4. Manabu Asai & Michael McAleer & Jun Yu, 2006. "Multivariate Stochastic Volatility," Microeconomics Working Papers 22058, East Asian Bureau of Economic Research.
    5. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    6. 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.
    7. Siddhartha Chib & Yasuhiro Omori & Manabu Asai, 2007. "Multivariate stochastic volatility (Revised in May 2007, Handbook of Financial Time Series (Published in "Handbook of Financial Time Series" (eds T.G. Andersen, R.A. Davis, Jens-Peter Kreiss," CARF F-Series CARF-F-094, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    8. 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.
    9. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3674-3689.
    10. 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.
    11. 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.
    12. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    13. 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.
    14. 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.
    15. Moura, Guilherme V. & Santos, André A. P., 2019. "Comparing Forecasts of Extremely Large Conditional Covariance Matrices," DES - Working Papers. Statistics and Econometrics. WS 29291, Universidad Carlos III de Madrid. Departamento de Estadística.
    16. Asai, Manabu & Caporin, Massimiliano & McAleer, Michael, 2015. "Forecasting Value-at-Risk using block structure multivariate stochastic volatility models," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 40-50.
    17. Gribisch, Bastian, 2013. "A latent dynamic factor approach to forecasting multivariate stock market volatility," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79823, Verein für Socialpolitik / German Economic Association.
    18. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    19. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    20. M. Hakan Eratalay, 2016. "Estimation of Multivariate Stochastic Volatility Models: A Comparative Monte Carlo Study," International Econometric Review (IER), Econometric Research Association, vol. 8(2), pages 19-52, September.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tky:fseres:2014cf938. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: CIRJE administrative office (email available below). General contact details of provider: https://edirc.repec.org/data/ritokjp.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.