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Cholesky Realized Stochasti Volatility Model

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  • Shinichiro Shirota
  • Yashiro Omori
  • Hedibert Lopes
  • Haixiang Piao

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 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 attain 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, we propose a flexible modeling for stylized facts of financial markets such as dynamic correlations and leverage effects among volatilities. Taking a Bayesian approach, we describe Markov Chain Monte Carlo implementation with a simple but efficient sampling scheme. Our model is applied to nine U.S. stock returns data, and the model comparison is conducted based on portfolio performances.

Suggested Citation

  • Shinichiro Shirota & Yashiro Omori & Hedibert Lopes & Haixiang Piao, 2016. "Cholesky Realized Stochasti Volatility Model," Business and Economics Working Papers 224, Unidade de Negocios e Economia, Insper.
    • Handle: RePEc:aap:wpaper:224
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    References listed on IDEAS

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    1. repec:hal:journl:peer-00815564 is not listed on IDEAS
    2. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
    3. Geweke, John & Zhou, Guofu, 1996. "Measuring the Pricing Error of the Arbitrage Pricing Theory," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 557-587.
    4. Shirota, Shinichiro & Hizu, Takayuki & Omori, Yasuhiro, 2014. "Realized stochastic volatility with leverage and long memory," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 618-641.
    5. Berger, James O. & Yang, Ruo-Yong, 1994. "Noninformative Priors and Bayesian Testing for the AR(1) Model," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 461-482, August.
    6. Barndorff-Nielsen, Ole E. & Hansen, Peter Reinhard & Lunde, Asger & Shephard, Neil, 2011. "Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading," Journal of Econometrics, Elsevier, vol. 162(2), pages 149-169, June.
    7. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    8. 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.
    9. Venter, J.H. & de Jongh, P.J., 2014. "Extended stochastic volatility models incorporating realised measures," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 687-707.
    10. 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.
    11. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    12. Andrew Harvey & Esther Ruiz & Neil Shephard, 1994. "Multivariate Stochastic Variance Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(2), pages 247-264.
    13. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2006. "Analysis of high dimensional multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 134(2), pages 341-371, October.
    14. Engle, Robert & Colacito, Riccardo, 2006. "Testing and Valuing Dynamic Correlations for Asset Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 238-253, April.
    15. 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.
    16. Yufeng Han, 2006. "Asset Allocation with a High Dimensional Latent Factor Stochastic Volatility Model," The Review of Financial Studies, Society for Financial Studies, vol. 19(1), pages 237-271.
    17. Takahashi, Makoto & Omori, Yasuhiro & Watanabe, Toshiaki, 2009. "Estimating stochastic volatility models using daily returns and realized volatility simultaneously," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2404-2426, April.
    18. 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.
    19. Tingguo Zheng & Tao Song, 2014. "A Realized Stochastic Volatility Model With Box-Cox Transformation," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 593-605, October.
    20. 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.
    21. Aguilar, Omar & West, Mike, 2000. "Bayesian Dynamic Factor Models and Portfolio Allocation," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 338-357, July.
    22. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    23. Alexander Philipov & Mark Glickman, 2006. "Factor Multivariate Stochastic Volatility via Wishart Processes," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 311-334.
    24. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    25. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    26. 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.
    27. 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.
    28. Lubrano, Michel, 1995. "Testing for unit roots in a Bayesian framework," Journal of Econometrics, Elsevier, vol. 69(1), pages 81-109, September.
    29. Asai, Manabu & McAleer, Michael, 2009. "The structure of dynamic correlations in multivariate stochastic volatility models," Journal of Econometrics, Elsevier, vol. 150(2), pages 182-192, June.
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