A Multivariate Stable Model for the Distribution of Portfolio Returns

In this paper we combine the appealing properties of the stable Paretian distribution to model the heavy tails and the GARCH model to capture the phenomenon of the volatility clustering. We assume the asset-returns to have a particular multivariate stable distribution, i.e., to be sub-Gaussian random vectors. In this way the characteristic function has a tractable expression and the density function can be recovered by using the Fast Fourier Transform and linear interpolation. A multivariate GARCH structure is then adopted to model the covariance matrix of the Gaussian vectors underlying the sub-Gaussian system. Finally, the model is applied to daily U.S. stock returns. ∗E-mail address: [email protected].