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A hierarchical Archimedean copula for portfolio credit risk modelling

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  • Puzanova, Natalia

Abstract

I introduce a novel, hierarchical model of tail dependent asset returns which can be particularly useful for measuring portfolio credit risk within the structural framework. To allow for a stronger dependence within sub-portfolios than between them, I utilise the concept of nested Archimedean copulas, but modify the nesting procedure to ensure the compatibility of copula generators by construction. This makes sampling straightforward. Moreover, I provide details on a particular specification based on a gamma mixture of powers. This model allows for lower tail dependence, resulting in a more conservative credit risk assessment than a comparable Gaussian model. I illustrate the extent of model risk when calculating VaR or Expected Shortfall for a credit portfolio.

Suggested Citation

  • Puzanova, Natalia, 2011. "A hierarchical Archimedean copula for portfolio credit risk modelling," Discussion Paper Series 2: Banking and Financial Studies 2011,14, Deutsche Bundesbank.
    • Handle: RePEc:zbw:bubdp2:201114
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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.
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    Cited by:

    1. Segers, Johan & Uyttendaele, Nathan, 2014. "Nonparametric estimation of the tree structure of a nested Archimedean copula," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 190-204.
    2. Tente, Natalia & von Westernhagen, Natalja & Slopek, Ulf, 2017. "M-PRESS-CreditRisk: A holistic micro- and macroprudential approach to capital requirements," Discussion Papers 15/2017, Deutsche Bundesbank.
    3. Natalia Tente & Natalja Von Westernhagen & Ulf Slopek, 2019. "M‐PRESS‐CreditRisk: Microprudential and Macroprudential Capital Requirements for Credit Risk under Systemic Stress," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 51(7), pages 1923-1961, October.
    4. Yong Ma & Zhengjun Zhang & Weiguo Zhang & Weidong Xu, 2015. "Evaluating the Default Risk of Bond Portfolios with Extreme Value Theory," Computational Economics, Springer;Society for Computational Economics, vol. 45(4), pages 647-668, April.
    5. Antonov I. N. & Knyazev A. G. & Lepekhin O. A., 2016. "Copula Models of the Joint Distribution of Exchange Rates," World of economics and management / Vestnik NSU. Series: Social and Economics Sciences, Socionet, vol. 16(4), pages 20-38.
    6. Segers, Johan & Uyttendaele, Nathan, 2013. "Nonparametric estimation of the tree structure of a nested Archimedean copula," LIDAM Discussion Papers ISBA 2013009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    7. Knyazev, Alexander & Lepekhin, Oleg & Shemyakin, Arkady, 2016. "Joint distribution of stock indices: Methodological aspects of construction and selection of copula models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 30-53.

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    More about this item

    Keywords

    portfolio credit risk; nested Archimedean copula; tail dependence; hierarchical dependence structure;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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