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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. 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.
    3. 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.
    4. Stephan Höcht & Rudi Zagst, 2010. "Pricing distressed CDOs with stochastic recovery," Review of Derivatives Research, Springer, vol. 13(3), pages 219-244, October.
    5. 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.
    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. Mai, Jan-Frederik & Scherer, Matthias, 2012. "H-extendible copulas," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 151-160.
    2. Sabrina Mulinacci, 2017. "A systemic shock model for too big to fail financial institutions," Papers 1704.02160, arXiv.org, revised Apr 2017.
    3. 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.
    4. 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).
    5. 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.
    6. 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.
    7. Sabrina Mulinacci, 2015. "Archimedean-based Marshall-Olkin Distributions and Related Copula Functions," Papers 1502.01912, arXiv.org.
    8. 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.
    9. Umberto Cherubini & Sabrina Mulinacci, 2015. "Systemic Risk with Exchangeable Contagion: Application to the European Banking System," Papers 1502.01918, arXiv.org.

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