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Approximating correlated defaults

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  • Rosenthal, Dale W.R.

Abstract

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.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 36788.

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Date of creation: 2008
Date of revision: 15 Feb 2012
Handle: RePEc:pra:mprapa:36788

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Related research

Keywords: default approximating portfolio; diversity score; gamma Edgeworth expansion;

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References

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  1. Sanjiv Das & Darrell Duffie & Nikunj Kapadia & Leandro Saita, 2006. "Common Failings: How Corporate Defaults are Correlated," NBER Working Papers 11961, National Bureau of Economic Research, Inc.
  2. Darrell DUFFIE & Andreas ECKNER & Guillaume HOREL & Leandro SAITA, . "Frailty Correlated Default," Swiss Finance Institute Research Paper Series, Swiss Finance Institute 08-44, Swiss Finance Institute.
  3. Robert A. Jarrow, 2001. "Counterparty Risk and the Pricing of Defaultable Securities," Journal of Finance, American Finance Association, American Finance Association, vol. 56(5), pages 1765-1799, October.
  4. Jarrow, Robert A & Lando, David & Turnbull, Stuart M, 1997. "A Markov Model for the Term Structure of Credit Risk Spreads," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 10(2), pages 481-523.
  5. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  6. Zhou, Chunsheng, 2001. "An Analysis of Default Correlations and Multiple Defaults," Review of Financial Studies, Society for Financial Studies, Society for Financial Studies, vol. 14(2), pages 555-76.
  7. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, American Finance Association, vol. 31(2), pages 351-67, May.
  8. P. Collin-Dufresne & R. Goldstein & J. Hugonnier, 2004. "A General Formula for Valuing Defaultable Securities," Econometrica, Econometric Society, Econometric Society, vol. 72(5), pages 1377-1407, 09.
  9. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 50(1), pages 53-85, March.
  10. Giesecke, Kay, 2006. "Default and information," Journal of Economic Dynamics and Control, Elsevier, Elsevier, vol. 30(11), pages 2281-2303, November.
  11. 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, American Finance Association, vol. 51(3), pages 987-1019, July.
  12. Ingo Fender & John Kiff, 2004. "CDO rating methodology: Some thoughts on model risk and its implications," BIS Working Papers 163, Bank for International Settlements.
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