Skew Generalized Secant Hyperbolic Distributions: Unconditional and Conditional Fit to Asset Returns

Abstract

A generalization of the hyperbolic secant distribution which allows for both skewness and leptokurtosis was given by Morris (1982). Recently, Vaughan (2002) proposed another flexible generalization of the hyperbolic secant distribution which has a lot of nice properties but is not able to allow for skewness. For this reason, Fischer and Vaughan (2002) additionally introduced a skewness parameter by means of splitting the scale parameter and showed that most of the nice properties are preserved. We briefly reviewthis class of distributions and apply them to financial return data. By means of the Nikkei225 data, it will be shown that this class of distributions, the socalled skew generalized secant hyperbolic distribution, provides an excellent fit in the context of unconditional and conditional return models.