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Systemic Risk with Exchangeable Contagion: Application to the European Banking System

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  • Umberto Cherubini
  • Sabrina Mulinacci

Abstract

We propose a model and an estimation technique to distinguish systemic risk and contagion in credit risk. The main idea is to assume, for a set of $d$ obligors, a set of $d$ idiosyncratic shocks and a shock that triggers the default of all them. All shocks are assumed to be linked by a dependence relationship, that in this paper is assumed to be exchangeable and Archimedean. This approach is able to encompass both systemic risk and contagion, with the Marshall-Olkin pure systemic risk model and the Archimedean contagion model as extreme cases. Moreover, we show that assuming an affine structure for the intensities of idiosyncratic and systemic shocks and a Gumbel copula, the approach delivers a complete multivariate distribution with exponential marginal distributions. The model can be estimated by applying a moment matching procedure to the bivariate marginals. We also provide an easy visual check of the good specification of the model. The model is applied to a selected sample of banks for 8 European countries, assuming a common shock for every country. The model is found to be well specified for 4 of the 8 countries. We also provide the theoretical extension of the model to the non-exchangeable case and we suggest possible avenues of research for the estimation.

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  • Umberto Cherubini & Sabrina Mulinacci, 2015. "Systemic Risk with Exchangeable Contagion: Application to the European Banking System," Papers 1502.01918, arXiv.org.
    • Handle: RePEc:arx:papers:1502.01918
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    References listed on IDEAS

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    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.
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    Cited by:

    1. Ostap Okhrin & Alexander Ristig & Jeffrey Sheen & Stefan Trück, 2015. "Conditional Systemic Risk with Penalized Copula," SFB 649 Discussion Papers SFB649DP2015-038, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    2. Damjana Kokol Bukovv{s}ek & Tomav{z} Kov{s}ir & Blav{z} Mojv{s}kerc & Matjav{z} Omladiv{c}, 2018. "Asymmetric linkages: maxmin vs. reflected maxmin copulas," Papers 1808.07737, arXiv.org, revised Jul 2019.
    3. 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.
    4. Damjana Kokol Bukovv{s}ek & Tomav{z} Kov{s}ir & Blav{z} Mojv{s}kerc & Matjav{z} Omladiv{c}, 2018. "Non-exchangeability of copulas arising from shock models," Papers 1808.09698, arXiv.org, revised Jul 2019.

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