IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v77y2017icp38-48.html
   My bibliography  Save this article

Remarks on composite Bernstein copula and its application to credit risk analysis

Author

Listed:
  • Guo, Nan
  • Wang, Fang
  • Yang, Jingping

Abstract

The composite Bernstein copula (CBC) (Yang et al., 2015) is a copula function generated from a composition of two copulas. This paper first shows that some well-known copulas belong to the CBC family with desirable properties. An EM algorithm for estimating the CBC is proposed, and it is applied for a real dataset to show the fitting result of the CBC in modeling dependence. The probabilistic structure for the CBC family is presented, which is useful for generating random numbers from the CBC. Finally, the probabilistic structure of the CBC is applied to credit risk analysis of collateralized debt obligations to show its advantage in empirical analysis.

Suggested Citation

  • Guo, Nan & Wang, Fang & Yang, Jingping, 2017. "Remarks on composite Bernstein copula and its application to credit risk analysis," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 38-48.
    • Handle: RePEc:eee:insuma:v:77:y:2017:i:c:p:38-48
    DOI: 10.1016/j.insmatheco.2017.08.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668717301944
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2017.08.007?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Yang, Jingping & Chen, Zhijin & Wang, Fang & Wang, Ruodu, 2015. "Composite Bernstein Copulas," ASTIN Bulletin, Cambridge University Press, vol. 45(2), pages 445-475, May.
    2. Avanzi, Benjamin & Cassar, Luke C. & Wong, Bernard, 2011. "Modelling Dependence in Insurance Claims Processes with Lévy Copulas," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 575-609, November.
    3. Benmelech, Efraim & Dlugosz, Jennifer, 2009. "The alchemy of CDO credit ratings," Journal of Monetary Economics, Elsevier, vol. 56(5), pages 617-634, July.
    4. Kay Giesecke & Baeho Kim, 2011. "Risk Analysis of Collateralized Debt Obligations," Operations Research, INFORMS, vol. 59(1), pages 32-49, February.
    5. Tavin, Bertrand, 2015. "Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 158-178.
    6. Diers, Dorothea & Eling, Martin & Marek, Sebastian D., 2012. "Dependence modeling in non-life insurance using the Bernstein copula," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 430-436.
    7. K. Bayramoglu & I. Bayramoglu (Bairamov), 2014. "Baker- Lin-Huang Type Bivariate Distributions Based on Order Statistics," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(10-12), pages 1992-2006, May.
    8. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    9. Bairamov, I. & Bayramoglu, K., 2013. "From the Huang–Kotz FGM distribution to Baker’s bivariate distribution," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 106-115.
    10. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    11. Shi, Peng & Frees, Edward W., 2011. "Dependent Loss Reserving using Copulas," ASTIN Bulletin, Cambridge University Press, vol. 41(2), pages 449-486, November.
    12. Dou, Xiaoling & Kuriki, Satoshi & Lin, Gwo Dong & Richards, Donald, 2016. "EM algorithms for estimating the Bernstein copula," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 228-245.
    13. Gregor Wei{ss} & Marcus Scheffer, 2012. "Smooth Nonparametric Bernstein Vine Copulas," Papers 1210.2043, arXiv.org.
    14. Bertrand Tavin, 2015. "Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals," Post-Print hal-02313250, HAL.
    15. Sancetta, Alessio, 2007. "Online forecast combinations of distributions: Worst case bounds," Journal of Econometrics, Elsevier, vol. 141(2), pages 621-651, December.
    16. Lin, G.D. & Huang, J.S., 2010. "A note on the maximum correlation for Baker's bivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2227-2233, October.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lautier, Jackson P. & Pozdnyakov, Vladimir & Yan, Jun, 2023. "Pricing time-to-event contingent cash flows: A discrete-time survival analysis approach," Insurance: Mathematics and Economics, Elsevier, vol. 110(C), pages 53-71.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Cheung, Eric C.K. & Peralta, Oscar & Woo, Jae-Kyung, 2022. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Insurance: Mathematics and Economics, Elsevier, vol. 106(C), pages 364-389.
    2. Masuhr Andreas & Trede Mark, 2020. "Bayesian estimation of generalized partition of unity copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 119-131, January.
    3. Eric C. K. Cheung & Oscar Peralta & Jae-Kyung Woo, 2021. "Multivariate matrix-exponential affine mixtures and their applications in risk theory," Papers 2201.11122, arXiv.org.
    4. Masuhr Andreas & Trede Mark, 2020. "Bayesian estimation of generalized partition of unity copulas," Dependence Modeling, De Gruyter, vol. 8(1), pages 119-131, January.
    5. Shahid Latif & Slobodan P. Simonovic, 2022. "Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(14), pages 5599-5632, November.
    6. Dou, Xiaoling & Kuriki, Satoshi & Lin, Gwo Dong & Richards, Donald, 2016. "EM algorithms for estimating the Bernstein copula," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 228-245.
    7. Blier-Wong, Christopher & Cossette, Hélène & Marceau, Etienne, 2023. "Risk aggregation with FGM copulas," Insurance: Mathematics and Economics, Elsevier, vol. 111(C), pages 102-120.
    8. Benjamin Avanzi & Gregory Clive Taylor & Bernard Wong & Xinda Yang, 2020. "On the modelling of multivariate counts with Cox processes and dependent shot noise intensities," Papers 2004.11169, arXiv.org, revised Dec 2020.
    9. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2017. "The empirical beta copula," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 35-51.
    10. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Papers 2103.10989, arXiv.org.
    11. Tavin, Bertrand, 2015. "Detection of arbitrage in a market with multi-asset derivatives and known risk-neutral marginals," Journal of Banking & Finance, Elsevier, vol. 53(C), pages 158-178.
    12. Fouad Marri & Khouzeima Moutanabbir, 2021. "Risk aggregation and capital allocation using a new generalized Archimedean copula," Working Papers hal-03169291, HAL.
    13. Daniel Bartl & Michael Kupper & Thibaut Lux & Antonis Papapantoleon & Stephan Eckstein, 2017. "Marginal and dependence uncertainty: bounds, optimal transport, and sharpness," Papers 1709.00641, arXiv.org, revised Aug 2018.
    14. Andreas Masuhr, 2018. "Bayesian Estimation of Generalized Partition of Unity Copulas," CQE Working Papers 7318, Center for Quantitative Economics (CQE), University of Muenster.
    15. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    16. Bairamov, I. & Bayramoglu, K., 2013. "From the Huang–Kotz FGM distribution to Baker’s bivariate distribution," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 106-115.
    17. Araichi, Sawssen & Peretti, Christian de & Belkacem, Lotfi, 2017. "Reserve modelling and the aggregation of risks using time varying copula models," Economic Modelling, Elsevier, vol. 67(C), pages 149-158.
    18. Huang, J.S. & Dou, Xiaoling & Kuriki, Satoshi & Lin, G.D., 2013. "Dependence structure of bivariate order statistics with applications to Bayramoglu’s distributions," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 201-208.
    19. Durante, Fabrizio & Sánchez, Juan Fernández, 2012. "On the approximation of copulas via shuffles of Min," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1761-1767.
    20. Segers, Johan & Sibuya, Masaaki & Tsukahara, Hideatsu, 2016. "The Empirical Beta Copula," LIDAM Discussion Papers ISBA 2016032, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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:eee:insuma:v:77:y:2017:i:c:p:38-48. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.