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

A generalization of the hyperbolic secant distribution which allows bothfor skewness and for leptokurtosis was given by Morris (1982). Recently,Vaughan (2002) proposed another flexible generalization of the hyperbolic secantdistribution which has a lot of nice properties but is not able to allowfor skewness. For this reason, Fischer and Vaughan (2002) additionally introduceda skewness parameter by means of splitting the scale parameter andshowed that most of the nice properties are preserved. We briefly review bothclasses of distributions and apply them to financial return data. By means ofthe Nikkei225 data, it will be shown that this class of distributions – the socalledskew generalized secant hyperbolic distribution – provides an excellentfit in the context of unconditional and conditional return models.