文章基本信息

标题：Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions
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作者：Maria Grazia Zoia ; Gianmarco Vacca ; Laura Barbieri 等
期刊名称：Risks
印刷版ISSN：2227-9091
出版年度：2020
卷号：8
期号：123
页码：123
DOI：10.3390/risks8040123
语种：English
出版社：MDPI, Open Access Journal
摘要：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.