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.
Inglese
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]
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10807/145294
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