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Multivariate Stochastic Volatility

  • Siddhartha ChibEmail author
  • Yasuhiro Omori
  • Manabu Asai
Chapter

Abstract

We provide a detailed summary of the large and vibrant emerging literature that deals with the multivariate modeling of conditional volatility of financial time series within the framework of stochastic volatility. The developments and achievements in this area represent one of the great success stories of financial econometrics. Three broad classes of multivariate stochastic volatility models have emerged: one that is a direct extension of the univariate class of stochastic volatility model, another that is related to the factor models of multivariate analysis and a third that is based on the direct modeling of time-varying correlation matrices via matrix exponential transformations, Wishart processes and other means. We discuss each of the various model formulations, provide connections and differences and show how the models are estimated. Given the interest in this area, further significant developments can be expected, perhaps fostered by the overview and details delineated in this paper, especially in the fitting of high-dimensional models.

Keywords

Markov Chain Monte Carlo Stochastic Volatility Markov Chain Monte Carlo Algorithm Stochastic Volatility Model Full Conditional Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Washington University in St. LouisUSA
  2. 2.Faculty of EconomicsUniversity of TokyoBunkyo-KuJapan
  3. 3.Faculty of EconomicsSoka UniversityTangi-choJapan

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