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

Maria Zoia, Federica Nicolussi

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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 (CHS). 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 modelling heavy-tailed series and computing risk measures.
Original languageEnglish
Pages (from-to)N/A-N/A
JournalJournal of Statistical Theory and Practice
DOIs
Publication statusPublished - 2019

Keywords

  • Convoluted hyperbolic-secant distribution
  • kurtosis
  • orthogonal polynomials
  • skewness

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