Gram–Charlier-Like Expansions of the Convoluted Hyperbolic-Secant Density

  • Federica Nicolussi
  • Maria Grazia ZoiaEmail author
Original Article


Since financial series are usually heavy tailed and skewed, research has formerly considered well-known leptokurtic distributions to model these series and, recently, has focused on the technique of adjusting the moments of a probability law by using its orthogonal polynomials. This paper combines these approaches by modifying the moments of the convoluted hyperbolic secant. The resulting density is a Gram–Charlier-like (GC-like) expansion capable to account for skewness and excess kurtosis. Multivariate extensions of these expansions are obtained on an argument using spherical distributions. Both the univariate and multivariate (GC-like) expansions prove to be effective in modeling heavy-tailed series and computing risk measures.


Convoluted hyperbolic-secant distribution Orthogonal polynomials Kurtosis Skewness Gram–Charlier-like expansion 



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Copyright information

© Grace Scientific Publishing 2020

Authors and Affiliations

  1. 1.Department of Economics, Management and Quantitative MethodsUniversità degli Studi di MilanoMilanItaly
  2. 2.Department of Economic PolicyUniversità Cattolica del Sacro CuoreMilanItaly

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