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Factor Multivariate Stochastic Volatility via Wishart Processes

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  • 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. Christian Gourieroux & Joann Jasiak & Razvan Sufana, 2004. "The Wishart Autoregressive of Multivariate Stochastic Volatility," Working Papers 2004-32, Center for Research in Economics and Statistics.
    2. Ronald Mahieu & Peter C. Schotman, 1994. "Stochastic volatility and the distribution of exchange rate news," Discussion Paper / Institute for Empirical Macroeconomics 96, Federal Reserve Bank of Minneapolis.
    3. 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.
    4. 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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