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Valuation of collateralized debt obligations with hierarchical Archimedean copulae

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  • Choroś-Tomczyk, Barbara
  • Härdle, Wolfgang Karl
  • Okhrin, Ostap

Abstract

Modelling portfolio credit risk is one of the crucial challenges faced by financial services industry in the last few years. We propose the valuation model of collateralized debt obligations (CDO) based on hierarchical Archimedean copulae (HAC) with up to three parameters, with default intensities calibrated to market data and with random loss given defaults that are correlated with default times. The methods presented are used to reproduce the spreads of the iTraxx Europe tranches. Our approach describes the market prices better than the standard pricing procedure based on the Gaussian distribution. We also obtain a flat correlation smile across tranches thereby solving the implied correlation puzzle.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:empfin:v:24:y:2013:i:c:p:42-62
    DOI: 10.1016/j.jempfin.2013.08.001
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    10. Okhrin Ostap & Okhrin Yarema & Schmid Wolfgang, 2013. "Properties of hierarchical Archimedean copulas," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 21-54, March.
    11. Edward I. Altman & Brooks Brady & Andrea Resti & Andrea Sironi, 2005. "The Link between Default and Recovery Rates: Theory, Empirical Evidence, and Implications," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2203-2228, November.
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    Cited by:

    1. D. V. Boreiko & Y. M. Kaniovski & G. Ch. Pflug, 2016. "Modeling dependent credit rating transitions: a comparison of coupling schemes and empirical evidence," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 24(4), pages 989-1007, December.
    2. Bernardi Enrico & Romagnoli Silvia, 2015. "A copula-based hierarchical hybrid loss distribution," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 73-87, April.
    3. Meng-Jou Lu & Cathy Yi-Hsuan Chen & Wolfgang Karl Härdle, 2017. "Copula-based factor model for credit risk analysis," Review of Quantitative Finance and Accounting, Springer, vol. 49(4), pages 949-971, November.
    4. Stefan Hochrainer-Stigler & Juraj Balkovič & Kadri Silm & Anna Timonina-Farkas, 2019. "Large scale extreme risk assessment using copulas: an application to drought events under climate change for Austria," Computational Management Science, Springer, vol. 16(4), pages 651-669, October.
    5. D. V. Boreiko & Y. M. Kaniovski & G. Ch. Pflug, 2017. "Numerical Modeling of Dependent Credit Rating Transitions with Asynchronously Moving Industries," Computational Economics, Springer;Society for Computational Economics, vol. 49(3), pages 499-516, March.
    6. Zhu, Wenjun & Wang, Chou-Wen & Tan, Ken Seng, 2016. "Structure and estimation of Lévy subordinated hierarchical Archimedean copulas (LSHAC): Theory and empirical tests," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 20-36.
    7. 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.
    8. Anna Timonina & Stefan Hochrainer‐Stigler & Georg Pflug & Brenden Jongman & Rodrigo Rojas, 2015. "Structured Coupling of Probability Loss Distributions: Assessing Joint Flood Risk in Multiple River Basins," Risk Analysis, John Wiley & Sons, vol. 35(11), pages 2102-2119, November.
    9. Fang, Jun & Jiang, Fan & Liu, Yong & Yang, Jingping, 2020. "Copula-based Markov process," Insurance: Mathematics and Economics, Elsevier, vol. 91(C), pages 166-187.
    10. repec:hum:wpaper:sfb649dp2015-042 is not listed on IDEAS
    11. Meng-Jou Lu & Cathy Yi-Hsuan Chen & Wolfgang Karl Hardle, 2020. "Copula-Based Factor Model for Credit Risk Analysis," Papers 2009.12092, arXiv.org, revised Oct 2020.
    12. Okhrin, Ostap & Xu, Ya Fei, 2017. "A comparison study of pricing credit default swap index tranches with convex combination of copulae," The North American Journal of Economics and Finance, Elsevier, vol. 42(C), pages 193-217.

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    More about this item

    Keywords

    CDO; Multivariate distributions; Copulae; Correlation smile; Loss given default;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages

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