Journal
QUANTITATIVE FINANCE
Volume 16, Issue 7, Pages 1069-1087Publisher
ROUTLEDGE JOURNALS, TAYLOR & FRANCIS LTD
DOI: 10.1080/14697688.2015.1111522
Keywords
Elliptical distribution; Tempered stable distribution; Fractional calculus; C5; G12
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Funding
- Swiss National Science Foundation Sinergia grant 'Empirics of Financial Stability' [154445]
- Belgian Federal Science Policy Office (BELSPO)
- BELSPO - Marie Curie Actions from European Commission
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Elliptical distributions are useful for modelling multivariate data, multivariate normal and Student t distributions being two special classes. In this paper, we provide a definition for the elliptical tempered stable (ETS) distribution based on its characteristic function, which involves a unique spectral measure. This definition provides a framework for creating a connection between the infinite divisible distribution (in particular the ETS distribution) with fractional calculus. In addition, a definition for the ETS copula is discussed. A simulation study shows the accuracy of this definition, in comparison to the normal copula for measuring the dependency of data. An empirical study of stock market index returns for 20 countries shows the usefulness of the theoretical results.
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