IDEAS home Printed from https://ideas.repec.org/a/wsi/ijitdm/v15y2016i02ns021962201650005x.html
   My bibliography  Save this article

Distorted Copula-Based Probability Distribution of a Counting Hierarchical Variable: A Credit Risk Application

Author

Listed:
  • Enrico Bernardi

    (University of Bologna, Department of Statistics, Via Belle Arti 41, Bologna 40126, Italy)

  • Silvia Romagnoli

    (University of Bologna, Department of Statistics, Via Belle Arti 41, Bologna 40126, Italy)

Abstract

In this paper, we propose a novel approach for the computation of the probability distribution of a counting variable linked to a multivariate hierarchical Archimedean copula function. The hierarchy has a twofold impact: it acts on the aggregation step but also it determines the arrival policy of the random event. The novelty of this work is to introduce this policy, formalized as an arrival matrix, i.e., a random matrix of dependent 0–1 random variables, into the model. This arrival matrix represents the set of distorted (by the policy itself) combinatorial distributions of the event, i.e., of the most probable scenarios. To this distorted version of the CHC approach [see Ref. 7 and Ref. 27], we are now able to apply a pure hierarchical Archimedean dependence structure among variables. As an empirical application, we study the problem of evaluating the probability distribution of losses related to the default of various type of counterparts in a structured portfolio exposed to the credit risk of a selected set among the major banks of European area and to the correlations among these risks.

Suggested Citation

  • Enrico Bernardi & Silvia Romagnoli, 2016. "Distorted Copula-Based Probability Distribution of a Counting Hierarchical Variable: A Credit Risk Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 15(02), pages 285-310, March.
  • Handle: RePEc:wsi:ijitdm:v:15:y:2016:i:02:n:s021962201650005x
    DOI: 10.1142/S021962201650005X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021962201650005X
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2013. "On the structure and estimation of hierarchical Archimedean copulas," Journal of Econometrics, Elsevier, vol. 173(2), pages 189-204.
    2. Hofert, Marius & Maechler, Martin, 2011. "Nested Archimedean Copulas Meet R: The nacopula Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 39(i09).
    3. repec:wsi:ijtafx:v:05:y:2002:i:08:n:s0219024902001742 is not listed on IDEAS
    4. Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
    5. Valdez, Emiliano A., 2009. "On the Distortion of a Copula and its Margins," MPRA Paper 20524, University Library of Munich, Germany.
    6. repec:wsi:ijitdm:v:11:y:2012:i:06:n:s0219622012500320 is not listed on IDEAS
    7. Umberto Cherubini & Silvia Romagnoli, 2009. "Computing the Volume of n-Dimensional Copulas," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(4), pages 307-314.
    8. Choroś-Tomczyk, Barbara & Härdle, Wolfgang Karl & Okhrin, Ostap, 2013. "Valuation of collateralized debt obligations with hierarchical Archimedean copulae," Journal of Empirical Finance, Elsevier, vol. 24(C), pages 42-62.
    9. Hofert, Marius, 2008. "Sampling Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5163-5174, August.
    Full references (including those not matched with items on IDEAS)

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijitdm:v:15:y:2016:i:02:n:s021962201650005x. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Tai Tone Lim). General contact details of provider: http://www.worldscinet.com/ijitdm/ijitdm.shtml .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.