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Default models based on scale mixtures of Marshall-Olkin copulas: properties and applications

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  • German Bernhart
  • Marcos Escobar Anel
  • Jan-Frederik Mai
  • Matthias Scherer

Abstract

We present a unification of the Archimedean and the Lévy-frailty copula model for portfolio default models. The new default model exhibits a copula known as scale mixture of Marshall-Olkin copulas and an investigation of the dependence structure reveals that desirable properties of both original models are combined. This allows for a wider range of dependence patterns, while the analytical tractability is retained. Furthermore, simultaneous defaults and default clustering are incorporated. In addition, a hierarchical extension is presented which allows for a heterogeneous dependence structure. Finally, the model is applied to the pricing of CDO contracts. For this purpose, an efficient Laplace transform inversion approach is developed. Supporting a separation of marginal default probabilities and dependence structure, the model can be calibrated to CDS contracts in a first step. In a second step, the calibration of several parametric families to CDO contracts demonstrates a good fitting quality, which further emphasizes the suitability of the approach. Copyright Springer-Verlag 2013

Suggested Citation

  • 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.
    • Handle: RePEc:spr:metrik:v:76:y:2013:i:2:p:179-203
    DOI: 10.1007/s00184-012-0382-z
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    References listed on IDEAS

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    1. Marius Hofert & Matthias Scherer, 2011. "CDO pricing with nested Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 11(5), pages 775-787.
    2. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
    3. X. Burtschell & Jonathan Gregory & Jean-Paul Laurent, 2009. "A Comparative Analysis of CDO Pricing Models under the Factor Copula Framework," Post-Print hal-03676448, HAL.
    4. Kjersti Aas & Daniel Berg, 2009. "Models for construction of multivariate dependence - a comparison study," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 639-659.
    5. Stephan Höcht & Rudi Zagst, 2010. "Pricing distressed CDOs with stochastic recovery," Review of Derivatives Research, Springer, vol. 13(3), pages 219-244, October.
    6. Li, Haijun, 2009. "Orthant tail dependence of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 243-256, January.
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    Citations

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    Cited by:

    1. Choe, Geon Ho & Choi, So Eun & Jang, Hyun Jin, 2020. "Assessment of time-varying systemic risk in credit default swap indices: Simultaneity and contagiousness," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    2. Umberto Cherubini & Sabrina Mulinacci, 2015. "Systemic Risk with Exchangeable Contagion: Application to the European Banking System," Papers 1502.01918, arXiv.org.
    3. Mai, Jan-Frederik & Scherer, Matthias, 2012. "H-extendible copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 151-160.
    4. 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.
    5. Sabrina Mulinacci, 2022. "A Marshall-Olkin Type Multivariate Model with Underlying Dependent Shocks," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2455-2484, December.
    6. Charpentier, A. & Fougères, A.-L. & Genest, C. & Nešlehová, J.G., 2014. "Multivariate Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 118-136.
    7. Sabrina Mulinacci, 2015. "Archimedean-based Marshall-Olkin Distributions and Related Copula Functions," Papers 1502.01912, arXiv.org.
    8. Sabrina Mulinacci, 2017. "A systemic shock model for too big to fail financial institutions," Papers 1704.02160, arXiv.org, revised Apr 2017.
    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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