Modeling Fat Tails in Stock Returns: A Multivariate Stable-GARCH Approach
34 Pages Posted: 19 Sep 2007 Last revised: 3 Oct 2009
Date Written: September 2009
In this paper a new multivariate volatility model is proposed. It combines the appealing properties of the stable Paretian distribution to model the heavy tails with the GARCH model to capture the volatility clustering. We assume that multivariate asset-returns of financial stocks follow a sub-Gaussian distribution, which is a particular multivariate stable distribution. In this way the characteristic function of the fitted returns has a tractable expression and the density function can be recovered by numerical methods. A multivariate GARCH structure is then adopted to model the covariance matrix of the Gaussian vectors underlying the sub-Gaussian system. The model is applied to a bivariate series of daily U.S. stock returns. Value-at-Risk for long and short positions is computed and compared with the one obtained using the multivariate normal and the multivariate Student's t distribution. Finally, exploiting the recent developments in the vast dimensional time-varying covariances modeling, possible feasible extensions to higher dimensions are suggested and an illustrative example using the Dow Jones index components is presented.
Keywords: fat tails, stable Paretian distributions, multivariate statistics, Value-at-Risk, GARCH
JEL Classification: C13, C22, C16, C51, C53, G17
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