While much of classical statistical analysis is based on Gaussian distributional assumptions, statistical modeling with the Laplace distribution has gained importance in many applied fields. This phenomenon is rooted in the fact that, like the Gaussian, the Laplace distribution has many attractive properties. This paper investigates two methods of combining them and their use in modeling and predicting financial risk. Based on 25 daily stock return series, the empirical results indicate that the new models offer a plausible description of the data. They are also shown to be competitive with, or superior to, use of the hyperbolic distribution, which has gained some popularity in asset-return modeling and, in fact, also nests the Gaussian and Laplace.
GARCH hyperbolic distribution kurtosis Laplace distribution mixture distributions stock market returns