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Construction and sampling of Archimedean and nested Archimedean Lévy copulas

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  • Grothe, Oliver
  • Hofert, Marius

Abstract

The class of Archimedean Lévy copulas is considered with focus on the construction and sampling of the corresponding Lévy processes. Furthermore, the class of nested Archimedean Lévy copulas is introduced. This class allows one to model hierarchical dependences between Lévy processes. It also overcomes the symmetry of Archimedean Lévy copulas. Finally, a new sampling algorithm for multivariate Lévy processes with dependence structure specified by either Archimedean or nested Archimedean Lévy copulas is derived from a Marshall–Olkin-type algorithm. In contrast to the widely used conditional sampling method, this algorithm does not require (inverses of) conditional Lévy copulas to be known. It also does not suffer from an asymmetric bias introduced by the conditional sampling method in the Lévy framework.

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  • Grothe, Oliver & Hofert, Marius, 2015. "Construction and sampling of Archimedean and nested Archimedean Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 182-198.
    • Handle: RePEc:eee:jmvana:v:138:y:2015:i:c:p:182-198
    DOI: 10.1016/j.jmva.2014.12.004
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    2. Maximilian Coblenz & Simon Holz & Hans‐Jörg Bauer & Oliver Grothe & Rainer Koch, 2020. "Modelling fuel injector spray characteristics in jet engines by using vine copulas," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 863-886, August.
    3. Xu, Chi & Zheng, Chunling & Wang, Donghua & Ji, Jingru & Wang, Nuan, 2019. "Double correlation model for operational risk: Evidence from Chinese commercial banks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 516(C), pages 327-339.
    4. Vladimir Panov, 2017. "Series Representations for Multivariate Time-Changed Lévy Models," Methodology and Computing in Applied Probability, Springer, vol. 19(1), pages 97-119, March.
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    7. Riva-Palacio, Alan & Leisen, Fabrizio, 2021. "Compound vectors of subordinators and their associated positive Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 183(C).

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