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Multivariate Stochastic Volatility

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Handbook of Financial Time Series

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.

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Authors and Affiliations

  1. Washington University in St. Louis, 1 Brookings Dr., St. Louis, Campus Box 1133, MO 63130, USA

    Siddhartha Chib

  2. Faculty of Economics, University of Tokyo, 7-3-1 Hongo, 113-0033, Bunkyo-Ku, Tokyo, Japan

    Yasuhiro Omori

  3. Faculty of Economics, Soka University, 1-236, 192-8577, Tangi-cho, Hachioji-shi Tokyo, Japan

    Manabu Asai

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  1. Siddhartha Chib
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  2. Yasuhiro Omori
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  3. Manabu Asai
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Correspondence to Siddhartha Chib .

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    Chib, S., Omori, Y., Asai, M. (2009). Multivariate Stochastic Volatility. In: Mikosch, T., Kreiß, JP., Davis, R., Andersen, T. (eds) Handbook of Financial Time Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71297-8_16

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