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Approximating correlated defaults


  • Rosenthal, Dale W.R.


Modeling defaults is critical to risk management as well as pricing debt portfolios and portfolio derivatives. In the recent financial crisis, multi-billion-dollar losses resulted from correlated defaults that were improperly modeled. This paper proposes statistical approximations which are more general than those used previously, follow from an intensity-based risk-factor model, and allow consistent parameter esti- mation. The parameters imply an approximating portfolio of independent, identical-credit loans and characterize both average credit quality and default-relative diversification (aka the “diversity score”). Unlike previous approaches, these metrics are derived jointly from theory. The approach addresses weaknesses in the typical diversity score-based methods by allowing for fatter tails as well as loans differing in size and credit quality. The approximations may also be used to model complete portfolio default and help set capital adequacy requirements. An example shows how to estimate the approximating portfolio.

Suggested Citation

  • Rosenthal, Dale W.R., 2008. "Approximating correlated defaults," MPRA Paper 36788, University Library of Munich, Germany, revised 15 Feb 2012.
  • Handle: RePEc:pra:mprapa:36788

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    References listed on IDEAS

    1. Darrell Duffie & Andreas Eckner & Guillaume Horel & Leandro Saita, 2009. "Frailty Correlated Default," Journal of Finance, American Finance Association, vol. 64(5), pages 2089-2123, October.
    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. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453 World Scientific Publishing Co. Pte. Ltd..
    4. Robert A. Jarrow & Stuart M. Turnbull, 2008. "Pricing Derivatives on Financial Securities Subject to Credit Risk," World Scientific Book Chapters,in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 17, pages 377-409 World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Leland, Hayne E & Toft, Klaus Bjerre, 1996. " Optimal Capital Structure, Endogenous Bankruptcy, and the Term Structure of Credit Spreads," Journal of Finance, American Finance Association, vol. 51(3), pages 987-1019, July.
    7. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, vol. 72(5), pages 1377-1407, September.
    8. 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.
    9. 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..
    10. 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.
    11. Ingo Fender & John Kiff, 2004. "CDO rating methodology: Some thoughts on model risk and its implications," BIS Working Papers 163, Bank for International Settlements.
    12. Giesecke, Kay, 2006. "Default and information," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 2281-2303, November.
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    More about this item


    default approximating portfolio; diversity score; gamma Edgeworth expansion;

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation


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