Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258076 
Year of Publication: 
2020
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 4 [Article No.:] 123 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-21
Publisher: 
MDPI, Basel
Abstract: 
This paper develops an approach based on Gram-Charlier-like expansions for modeling financial series to take in due account features such as leptokurtosis. A Gram-Charlier-like expansion adjusts the moments of interest of a given distribution via its own orthogonal polynomials. This approach, formerly adopted for univariate series, is here extended to a multivariate context by means of spherical densities. Previous works proposed the Gram-Charlier of the multivariate Gaussian, obtained by using Hermite polynomials. This work shows how polynomial expansions of an entire class of spherical laws can be worked out with the aim of obtaining a wide set of leptokurtic multivariate distributions. A Gram-Charlier-like expansion is a distribution characterized by an additional parameter with respect to the parent spherical law. This parameter, which measures the increase in kurtosis due to the polynomial expansion, can be estimated so as to make the resulting distribution capable of describing the empirical kurtosis found in the data. An application of the Gram-Charlier-like expansions to a set of financial assets proves their effectiveness in modeling multivariate financial series and assessing risk measures, such as the value at risk and the expected shortfall.
Subjects: 
orthogonal polynomials
kurtosis
power raised hyperbolic-secant distributions
value at risk
expected shortfall
JEL: 
C01
C51
C58
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
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