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.
Zoia, M., Nicolussi, F., Gram–Charlier-Like Expansions of the Convoluted Hyperbolic-Secant Density, <<JOURNAL OF STATISTICAL THEORY AND PRACTICE>>, 2020; (N/A): N/A-N/A. [doi:10.1007/s42519-019-0081-4] [http://hdl.handle.net/10807/145294]
Gram–Charlier-Like Expansions of the Convoluted Hyperbolic-Secant Density
Zoia, Maria
;Nicolussi, Federica
2019
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.