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Multivariate Hierarchical Copulas with Shocks

Author

Listed:
  • Fabrizio Durante

    (Johannes Kepler University Linz)

  • Marius Hofert

    (Ulm University)

  • Matthias Scherer

    (Technische Universität München)

Abstract

A transformation to obtain new multivariate hierarchical copulas, starting with an arbitrary copula, is introduced. In addition to the hierarchical structure, the presented construction principle explicitly supports singular components. These may be interpreted as the effect of local or global shocks to the underlying random variables. A large spectrum of dependence patterns can be achieved by the presented transformation, which seems promising for practical applications. Moreover, copulas arising from this construction are similarly admissible with respect to analytical tractability and sampling routines as the original copula. Finally, several well-known families of copulas may be interpreted as special cases.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metcap:v:12:y:2010:i:4:d:10.1007_s11009-009-9134-6
    DOI: 10.1007/s11009-009-9134-6
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    References listed on IDEAS

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    1. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    2. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    3. Mai, Jan-Frederik & Scherer, Matthias, 2009. "Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1567-1585, August.
    4. Hofert, Marius, 2008. "Sampling Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5163-5174, August.
    5. Patricia Mariela Morillas, 2005. "A method to obtain new copulas from a given one," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 61(2), pages 169-184, April.
    6. Paul Embrechts, 2009. "Copulas: A Personal View," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(3), pages 639-650, September.
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    Cited by:

    1. Fabrizio Durante & Roberta Pappadà & Nicola Torelli, 2015. "Clustering of time series via non-parametric tail dependence estimation," Statistical Papers, Springer, vol. 56(3), pages 701-721, August.
    2. Umberto Cherubini & Sabrina Mulinacci, 2015. "Systemic Risk with Exchangeable Contagion: Application to the European Banking System," Papers 1502.01918, arXiv.org.
    3. 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.
    4. Paul Embrechts & Marius Hofert, 2011. "Comments on: Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 263-270, August.
    5. Durante, Fabrizio & Fernández Sánchez, Juan & Sempi, Carlo, 2013. "Multivariate patchwork copulas: A unified approach with applications to partial comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 897-905.
    6. Anna Timonina & Stefan Hochrainer‐Stigler & Georg Pflug & Brenden Jongman & Rodrigo Rojas, 2015. "Structured Coupling of Probability Loss Distributions: Assessing Joint Flood Risk in Multiple River Basins," Risk Analysis, John Wiley & Sons, vol. 35(11), pages 2102-2119, November.

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