The paper aims at reshaping the normal law to account for tail-thickness and asymmetry, of which there is plenty of evidence in financial data. The inspiration to address the issue was provided by the orthogonality of Hermite polynomials with the Gaussian density as a weight function, with the Gram-Charlier expansion as background. A solution is then devised accordingly, by embodying skewness and excess-kurtosis in a normal kernel, via third and forth-degree polynomial tune-up. Features of the densities so obtained are established in the main theorem of the paper. In addition, a glance is cast at the issue of embodying between-squares correlation, and a solution is outlined.

Zoia, M., Tailoring the Gaussian law for excess kurtosis and skewness by Hermite polynomials, <<COMMUNICATIONS IN STATISTICS. THEORY AND METHODS>>, 2010; 39 (Gennaio): 52-64. [doi:10.1080/03610920802696596] [http://hdl.handle.net/10807/20539]

Tailoring the Gaussian law for excess kurtosis and skewness by Hermite polynomials

Zoia, Maria
2010

Abstract

The paper aims at reshaping the normal law to account for tail-thickness and asymmetry, of which there is plenty of evidence in financial data. The inspiration to address the issue was provided by the orthogonality of Hermite polynomials with the Gaussian density as a weight function, with the Gram-Charlier expansion as background. A solution is then devised accordingly, by embodying skewness and excess-kurtosis in a normal kernel, via third and forth-degree polynomial tune-up. Features of the densities so obtained are established in the main theorem of the paper. In addition, a glance is cast at the issue of embodying between-squares correlation, and a solution is outlined.
2010
Inglese
Zoia, M., Tailoring the Gaussian law for excess kurtosis and skewness by Hermite polynomials, <<COMMUNICATIONS IN STATISTICS. THEORY AND METHODS>>, 2010; 39 (Gennaio): 52-64. [doi:10.1080/03610920802696596] [http://hdl.handle.net/10807/20539]
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/20539
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 18
  • ???jsp.display-item.citation.isi??? 18
social impact