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Factor Multivariate Stochastic Volatility via Wishart Processes

Author

Listed:
  • Alexander Philipov
  • Mark Glickman

Abstract

This paper proposes a high dimensional factor multivariate stochastic volatility (MSV) model in which factor covariance matrices are driven by Wishart random processes. The framework allows for unrestricted specification of intertemporal sensitivities, which can capture the persistence in volatilities, kurtosis in returns, and correlation breakdowns and contagion effects in volatilities. The factor structure allows addressing high dimensional setups used in portfolio analysis and risk management, as well as modeling conditional means and conditional variances within the model framework. Owing to the complexity of the model, we perform inference using Markov chain Monte Carlo simulation from the posterior distribution. A simulation study is carried out to demonstrate the efficiency of the estimation algorithm. We illustrate our model on a data set that includes 88 individual equity returns and the two Fama-French size and value factors. With this application, we demonstrate the ability of the model to address high dimensional applications suitable for asset allocation, risk management, and asset pricing.

Suggested Citation

  • Alexander Philipov & Mark Glickman, 2006. "Factor Multivariate Stochastic Volatility via Wishart Processes," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 311-334.
  • Handle: RePEc:taf:emetrv:v:25:y:2006:i:2-3:p:311-334
    DOI: 10.1080/07474930600713366
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    References listed on IDEAS

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    1. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
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    Citations

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    Cited by:

    1. Bastian Gribisch, 2016. "Multivariate Wishart stochastic volatility and changes in regime," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 443-473, October.
    2. repec:kap:apfinm:v:24:y:2017:i:3:d:10.1007_s10690-017-9231-4 is not listed on IDEAS
    3. Zhou, Xiaocong & Nakajima, Jouchi & West, Mike, 2014. "Bayesian forecasting and portfolio decisions using dynamic dependent sparse factor models," International Journal of Forecasting, Elsevier, vol. 30(4), pages 963-980.
    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. Deschamps, Philippe J., 2011. "Bayesian estimation of an extended local scale stochastic volatility model," Journal of Econometrics, Elsevier, vol. 162(2), pages 369-382, June.
    6. repec:nax:conyad:v:62:y:2017:i:3:p:924-940 is not listed on IDEAS
    7. repec:bla:irvfin:v:17:y:2017:i:3:p:479-490 is not listed on IDEAS
    8. K. Triantafyllopoulos, 2008. "Multivariate stochastic volatility with Bayesian dynamic linear models," Papers 0802.0214, arXiv.org.
    9. 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, Elsevier.
    10. Roberto Leon-Gonzalez, 2014. "Efficient Bayesian Inference in Generalized Inverse Gamma Processes for Stochastic Volatility," Working Paper series 19_14, Rimini Centre for Economic Analysis.
    11. Jin, Xin & Maheu, John M., 2016. "Bayesian semiparametric modeling of realized covariance matrices," Journal of Econometrics, Elsevier, vol. 192(1), pages 19-39.
    12. Shinichiro Shirota & Yasuhiro Omori & Hedibert. F. Lopes & Haixiang Piao, 2016. "Cholesky Realized Stochastic Volatility Model," CIRJE F-Series CIRJE-F-1019, CIRJE, Faculty of Economics, University of Tokyo.
    13. Monfort, Alain & Renne, Jean-Paul & Roussellet, Guillaume, 2015. "A Quadratic Kalman Filter," Journal of Econometrics, Elsevier, vol. 187(1), pages 43-56.
    14. 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.
    15. Shinichiro Shirota & Yasuhiro Omori & Hedibert. F. Lopes & Haixiang Piao, 2015. "Cholesky Realized Stochastic Volatility Model," CIRJE F-Series CIRJE-F-979, CIRJE, Faculty of Economics, University of Tokyo.
    16. Mike K. P. So & C. Y. Choi, 2009. "A threshold factor multivariate stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(8), pages 712-735.
    17. repec:nax:conyad:v:62:y:2017:i:3:p:941-957 is not listed on IDEAS
    18. Clark, Todd E. & Carriero, Andrea & Marcellino, Massimiliano, 2016. "Large Vector Autoregressions with Stochastic Volatility and Flexible Priors," Working Paper 1617, Federal Reserve Bank of Cleveland.
    19. Xiao, Yuewen & Ku, Yu-Cheng & Bloomfield, Peter & Ghosh, Sujit K., 2015. "On the degrees of freedom in MCMC-based Wishart models for time series data," Statistics & Probability Letters, Elsevier, vol. 98(C), pages 59-64.
    20. 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.
    21. repec:eee:ecosta:v:3:y:2017:i:c:p:34-59 is not listed on IDEAS
    22. 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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