A0542
Title: A geometric treatment of time-varying volatilities
Authors: Chulwoo Han - Durham University (United Kingdom) [presenting]
Abstract: A new framework for addressing multivariate time-varying volatilities is proposed. By employing the coordinate-free methods of differential geometry, our method 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. Based on our geometric framework, we develop a fundamental time-varying volatility model. Our model preserves the symmetry and positive definiteness of the covariance matrix as it evolves, without imposing any ad hoc restrictions. Its parsimonious specification makes it particularly suitable for large dimensional systems. Simulation studies suggest that our model possesses much of the nonlinear nature of covariance dynamics observed in the market. Applied to the US and the UK stock markets, the model performs well, especially in terms of risk measurement. Its superiority over other models, however, demands further evidence. 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.
