Alternative multivariate stable distributions and their applications to financial modeling

It is commonly accepted that the distribution of returns on many financial assets is nonnormal. Mandelbrot [5] and Fama [2] proposed the α-stable distribution for modeling stock returns. In [9] we find that the geometric summation scheme provides a better model for univariate stock index data than various stable alternatives, including the α-stable model. Here we extend the geometric summation model to multivariate settings which allows us to model portfolios of financial assets.