A geometric treatment of time-varying volatilities

Chulwoo Han (), Frank C. Park () and Jangkoo Kang ()
Additional contact information
Chulwoo Han: Durham University
Frank C. Park: Seoul National University
Jangkoo Kang: KAIST

Review of Quantitative Finance and Accounting, 2017, vol. 49, issue 4, No 8, 1141 pages

Abstract: 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.

Keywords: Multivariate volatility model; Differential geometry; Riemmanian metric; GARCH (search for similar items in EconPapers)
JEL-codes: C10 C32 C51 C53 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11156-017-0618-0

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