Generalized Hyperbolic Secant Distributions With Applications to Finance

Among the symmetrical distributions with an infinite domain, the most popular alternative to the normal variant is the logistic distribution as well as the Laplace or the double exponential distribution, which was first introduced in 1774. Occasionally, the Cauchy distribution is also used. Surprisingly, the hyperbolic secant distribution has led a charmed life, although Manoukian and Nadeau had already stated in 1988 that “... the hyperbolic-secant distribution ... has not received sufficient attention in the published literature and may be useful for students and practitioners.” During the last few years, however, several generalizations of the hyperbolic secant distribution have become popular in the context of financial return data because of its excellent fit. Nearly all of them are summarized within this Springer Brief.

Preface.- Hyperbolic Secant Distributions.- The GSH Distribution Family and Skew Versions.- The NEF-GHS or Meixner Distribution Family.- The BHS Distribution Family.- The SHS and SASHS Distribution Family.- Application to Finance.- R-Code: Fitting a BHS Distribution.

Matthias Fischer studied Mathematics at the University of Erlangen-Nürnberg. His dissertation focused on infinitely divisible distribution and its application to option pricing and was followed by a postdoctoral thesis on copula-based, time-varying patchwork distributions with applications to financial data. He has also published a number of papers and monographs, in particular on generalized hyperbolic secant distributions.