Flexible Multivariate GARCH Modeling With an Application to International Stock Markets

Olivier Ledoit, Pedro Santa-Clara and Michael Wolf


The goal of this paper is to estimate time-varying covariance matrices. Since the covariance matrix of financial returns is known to change through time and is an essential ingredient in risk management, portfolio selection, and tests of asset pricing models, this is a very important problem in practice. Our model of choice is the Diagonal-Vech version of the Multivariate GARCH(1,1) model. This is the most straightforward multivariate extension of the GARCH(1,1) model, which is the standard model in univariate volatility estimation. Unfortunately, the estimation of the general Diagonal-Vech model has proved to be numerically infeasible for dimensions higher than 5. The common approach has been to estimate more restrictive models which are tractable but may not conform to the data. Our contribution is to propose an alternative estimation method that is numerically feasible for large-scale problems, produces positive semi-definite conditional covariance matrices, and does not impose unrealistic a priori restrictions. We provide an empirical application in the context of international stock markets, comparing the new estimator to a number of existing ones.

Review of Economics and Statistics, Volume 85, Issue 3, August 2003, pages 735-747

Download full paper (Acrobat PDF - 221KB)

Download Zip file containing Matlab routines from the website of my co-author Michael Wolf in the Department of Economics of the University of Zurich

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