The HS-SAS and GSH-SAS Distribution as Model for Unconditional and Conditional Return Distributions

Abstract

We introduce two new skewed and leptokurtic distributions derived from the hyperbolic secant distribution and from Vaughan (2002)’s generalized hyperbolic distribution by use of the sinh-arcsinh transformation introduced in Jones and Pewsey (2009). Properties of these new distribution are given. Their flexibility for modeling financial return data is comparable to that of their most advanced peers. Contrary to the latter for both distributions a closed-form solution for the density, cumulative distribution and quantile function can be given.