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Hierarchical Archimedean Dependence in Common Shock Models

Author

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  • Umberto Cherubini

    (University of Bologna)

  • Sabrina Mulinacci

    (University of Bologna)

Abstract

In this paper we show how to extend a simple common shock model with Archimedean dependence of the hidden variables to the non-exchangeable case. The assumption is that the hidden risk factors are linked by a hierarchical Archimedean dependence structure, possibly fully nested. We give directions about how to implement the model and to address the issue that the hidden variables must be put in descending dependence order. We show how the model can be simplified in the Gumbel-Marshall-Olkin distribution in Cherubini and Mulinacci (2017), the only case in which exponential distribution of the observed variables is preserved.

Suggested Citation

  • Umberto Cherubini & Sabrina Mulinacci, 2021. "Hierarchical Archimedean Dependence in Common Shock Models," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 143-163, March.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09816-8
    DOI: 10.1007/s11009-020-09816-8
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    References listed on IDEAS

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    1. Jianhua Lin & Xiaohu Li, 2014. "Multivariate Generalized Marshall–Olkin Distributions and Copulas," Methodology and Computing in Applied Probability, Springer, vol. 16(1), pages 53-78, March.
    2. Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
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    6. Fabrizio Durante & Marius Hofert & Matthias Scherer, 2010. "Multivariate Hierarchical Copulas with Shocks," Methodology and Computing in Applied Probability, Springer, vol. 12(4), pages 681-694, December.
    7. German Bernhart & Marcos Escobar Anel & Jan-Frederik Mai & Matthias Scherer, 2013. "Default models based on scale mixtures of Marshall-Olkin copulas: properties and applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 179-203, February.
    8. Li, Haijun, 2009. "Orthant tail dependence of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 243-256, January.
    9. Sabrina Mulinacci, 2018. "Archimedean-based Marshall-Olkin Distributions and Related Dependence Structures," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 205-236, March.
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