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A geometric treatment of time-varying volatilities

Author

Listed:
  • Chulwoo Han

    (Durham University)

  • Frank C. Park

    (Seoul National University)

  • Jangkoo Kang

    (KAIST)

Abstract

In this article, we propose a new framework for addressing multivariate time-varying volatilities. By employing methods of differential geometry, our model respects the geometric structure of the covariance space, i.e., symmetry and positive definiteness, in a way that is independent of any local coordinate parametrization. Its parsimonious specification makes it particularly suitable for large dimensional systems. Simulation studies suggest that our model embraces much of the nonlinear behaviour of the covariance dynamics. Applied to the US and the UK stock markets, the model performs well, especially when applied to risk measurement. In a broad context, our framework presents a new approach treating nonlinear properties observed in the financial market, and numerous areas of application can be further considered.

Suggested Citation

  • Chulwoo Han & Frank C. Park & Jangkoo Kang, 2017. "A geometric treatment of time-varying volatilities," Review of Quantitative Finance and Accounting, Springer, vol. 49(4), pages 1121-1141, November.
    • Handle: RePEc:kap:rqfnac:v:49:y:2017:i:4:d:10.1007_s11156-017-0618-0
    DOI: 10.1007/s11156-017-0618-0
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    References listed on IDEAS

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    Cited by:

    1. Han, Chulwoo & Park, Frank C., 2022. "A geometric framework for covariance dynamics," Journal of Banking & Finance, Elsevier, vol. 134(C).

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    More about this item

    Keywords

    Multivariate volatility model; Differential geometry; Riemmanian metric; GARCH;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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