IDEAS home Printed from
   My bibliography  Save this book

Portfolio Credit Risk Modelling and CDO Pricing - Analytics and Implied Trees from CDO Tranches


  • Tao Peng


One of the most successful and most controversial innovative financial products in recent years has been collateralised debt obligations (CDOs). The dimensionality of dependency embedded in a typical CDO structure poses great challenges for researchers - in both generating realistic default dynamics and correlation, and in the mean time achieving fast and accurate model calibration. The research presented in this thesis contributes to the class of bottom-up models, which, as opposed to top-down models, start by modelling the individual obligor default process and then moving them up through the dependency structures to build up the loss distributions at the portfolio level. The Gaussian model (Li 2000) is a static copula model. It has only on correlation parameter, which can be calibrated to one CDO tranche at a time. Its simplicity achieves wide spread industry application even though it suffers from the problem of ’correlation smile’. In other words, it cannot fit the market in an arbitrage-free manner in the capital-structure dimension. The first contribution of this thesis is the sensitivities analysis with regard to model parameters of expected losses of CDO tranches in the Gaussian and NIG copula models. The study provided substantial insight into the essence of the dependency structure. In addition, we apply the intensity approach to credit modelling in order to imply market distributions non-parametrically in the form of a binomial lattice. Under the same framework, we developed a series of three models. The static binomial model can be calibrated to the CDS index tranches exactly, with one set of parameters. The model can be seen as a non-parametric copula model that is arbitrage free in the capital-structure dimension. Static models are not suitable to price portfolio credit derivatives that are dynamic in nature. The static model can be naturally developed into a dynamic binomial model and satisfies no-arbitrage conditions in the time dimension. This setup, however, reduces model flexibility and calibration speed. The computational complexity comes from the non-Markovian character of the default process in the dynamic model. Inspired by Mortensen (2006), in which the author defines the intensity integral as a conditioning variable, we modify the dynamic model into a Markovian model by modelling the intensity integral directly, which greatly reduces the computational time and increases model fit in calibration. We also show that, when stochastic recovery rates are involved, there is a third no-arbitrage condition for the expected loss process that needs to be built into the Markovian model. For all binomial models, we adopt a unique optimisation algorithm for model calibration - the Cross Entropy method. It is particularly advantageous in solving large-scale non-linear optimsation problems with multiple local extrema, as encountered in our model.

Suggested Citation

  • Tao Peng, 2010. "Portfolio Credit Risk Modelling and CDO Pricing - Analytics and Implied Trees from CDO Tranches," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 8.
  • Handle: RePEc:uts:finphd:8

    Download full text from publisher

    File URL:
    Download Restriction: no

    References listed on IDEAS

    1. Giesecke, Kay & Weber, Stefan, 2006. "Credit contagion and aggregate losses," Journal of Economic Dynamics and Control, Elsevier, vol. 30(5), pages 741-767, May.
    2. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    3. Crane, Glenis & van der Hoek, John, 2008. "Using distortions of copulas to price synthetic CDOs," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 903-908, June.
    4. Duffie, Darrell & Singleton, Kenneth J, 1999. "Modeling Term Structures of Defaultable Bonds," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 687-720.
    5. David Heath & Robert Jarrow & Andrew Morton, 2008. "Bond Pricing And The Term Structure Of Interest Rates: A New Methodology For Contingent Claims Valuation," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 13, pages 277-305 World Scientific Publishing Co. Pte. Ltd..
    6. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    7. Philippe Ehlers & Philipp J. Schonbucher, 2006. "Pricing Interest Rate-SensitiveCredit Portfolio Derivatives," Swiss Finance Institute Research Paper Series 06-39, Swiss Finance Institute, revised Dec 2006.
    8. Philipp J. Schonbucher, 1997. "Team Structure Modelling of Defaultable Bonds," FMG Discussion Papers dp272, Financial Markets Group.
    9. Patrick Hagan & Graeme West, 2006. "Interpolation Methods for Curve Construction," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(2), pages 89-129.
    10. Stefan Weber & Kay Giesecke, 2003. "Credit Contagion and Aggregate Losses," Computing in Economics and Finance 2003 246, Society for Computational Economics.
    11. Sanjiv R. Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2007. "Common Failings: How Corporate Defaults Are Correlated," Journal of Finance, American Finance Association, vol. 62(1), pages 93-117, February.
    12. Robert A. Jarrow & Fan Yu, 2008. "Counterparty Risk and the Pricing of Defaultable Securities," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 20, pages 481-515 World Scientific Publishing Co. Pte. Ltd..
    13. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," Review of Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-576.
    14. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    15. Esa Jokivuolle & Samu Peura, 2003. "Incorporating Collateral Value Uncertainty in Loss Given Default Estimates and Loan-to-value Ratios," European Financial Management, European Financial Management Association, vol. 9(3), pages 299-314.
    16. Jeffery D Amato & Jacob Gyntelberg, 2005. "CDS index tranches and the pricing of credit risk correlations," BIS Quarterly Review, Bank for International Settlements, March.
    Full references (including those not matched with items on IDEAS)

    More about this item


    Access and download statistics


    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:uts:finphd:8. 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: (Duncan Ford). General contact details of provider: .

    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.