wHS-type distributions with application to finance

Abstract

We introduce several distribution families which all generalize the standard hyperbolic secant distribution and allow for flexible modelling of skewness and kurtosis. Due to the construction scheme as distorted hyperbolics secant families (where distortion functions are restricted to different flexible two-parametric families on the unit interval), both pdf, cdf and quantile function (qf) admit a closed-form for most of the families under consideration. In order to compare flexibility, goodness-of-fit measures are calculated for Nikkei225 data and compared to the results of well-known competitors.

Keywords:

• Hyperbolic secant distribution
• Financial returns
• Distortion function