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Multivariate Realized Stock Market Volatility

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  • Gregory Bauer
  • Keith Vorkink

Abstract

We present a new matrix-logarithm model of the realized covariance matrix of stock returns. The model uses latent factors which are functions of both lagged volatility and returns. The model has several advantages: it is parsimonious; it does not require imposing parameter restrictions; and, it results in a positive-definite covariance matrix. We apply the model to the covariance matrix of size-sorted stock returns and find that two factors are sufficient to capture most of the dynamics. We also introduce a new method to track an index using our model of the realized volatility covariance matrix.

Suggested Citation

  • Gregory Bauer & Keith Vorkink, 2007. "Multivariate Realized Stock Market Volatility," Staff Working Papers 07-20, Bank of Canada.
    • Handle: RePEc:bca:bocawp:07-20
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    1. Stanislav Anatolyev & Nikita Kobotaev, 2018. "Modeling and forecasting realized covariance matrices with accounting for leverage," Econometric Reviews, Taylor & Francis Journals, vol. 37(2), pages 114-139, February.
    2. Roxana Halbleib & Valerie Voev, 2011. "Forecasting Covariance Matrices: A Mixed Frequency Approach," Working Papers ECARES ECARES 2011-002, ULB -- Universite Libre de Bruxelles.
    3. Yin Liao & Heather Anderson & Farshid Vahid, 2010. "Do Jumps Matter? Forecasting Multivariate Realized Volatility Allowing for Common Jumps," ANU Working Papers in Economics and Econometrics 2010-520, Australian National University, College of Business and Economics, School of Economics.
    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. repec:hum:wpaper:sfb649dp2012-034 is not listed on IDEAS
    6. Matei, Marius, 2011. "Non-Linear Volatility Modeling of Economic and Financial Time Series Using High Frequency Data," Journal for Economic Forecasting, Institute for Economic Forecasting, vol. 0(2), pages 116-141, June.
    7. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    8. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.
    9. Florian Huber & Tamás Krisztin & Philipp Piribauer, 2017. "Forecasting Global Equity Indices Using Large Bayesian Vars," Bulletin of Economic Research, Wiley Blackwell, vol. 69(3), pages 288-308, July.
    10. 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.
    11. Michael McAleer & Marcelo Medeiros, 2008. "Realized Volatility: A Review," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 10-45.
    12. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    13. Härdle, Wolfgang Karl & Hautsch, Nikolaus & Pigorsch, Uta, 2008. "Measuring and modeling risk using high-frequency data," SFB 649 Discussion Papers 2008-045, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    14. Matteo Bonato & Massimiliano Caporin & Angelo Ranaldo, 2009. "Forecasting realized (co)variances with a block structure Wishart autoregressive model," Working Papers 2009-03, Swiss National Bank.
    15. Ilya Archakov & Peter Reinhard Hansen, 2021. "A New Parametrization of Correlation Matrices," Econometrica, Econometric Society, vol. 89(4), pages 1699-1715, July.
    16. 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.
    17. 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.

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    Keywords

    Econometric and statistical methods; Financial markets;

    JEL classification:

    • G14 - Financial Economics - - General Financial Markets - - - Information and Market Efficiency; Event Studies; Insider Trading
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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