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Credit Risk Modeling and the Term Structure of Credit Spreads

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  • Li Chen

    (Princeton University)

  • H. Vincent Poor

    (Princeton University)

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Abstract

In this paper, by applying the potential approach to characterizing default risk, a class of simple affine and quadratic models is presented to provide a unifying framework of valuing both risk-free and defaultable bonds. It has been shown that the established models can accommodate the existing intensity based credit risk models, while incorporating a security-specific credit information factor to capture the idiosyncratic default risk as well as the one from market-wide influence. The models have been calibrated using the integrated data of both treasury rates and the average bond yields in different rating classes. Filtering technique and the quasi maximum likelihood estimator (QMLE) are applied jointly to the problem of estimating the structural parameters of the affine and quadratic models. The asymptotic properties of the QMLE are analyzed under two criteria: asymptotic optimality under the Kullback-Leibler criterion, and consistency. Relative empirical performance of the two models has been investigated. It turns out that the quadratic model outperforms the affine model in explaining the historical yield behavior of both Treasury and corporate bonds, while producing a larger error in fitting cross-sectional bond spread curves. Moreover, a modified fat-tail affine model is also proposed to improve the cross-sectional term structure fitting abilities of the existing models. Meanwhile, our empirical study provides complete estimates of risk-premia for both market risk and credit default risk including jump event risk.

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File URL: http://128.118.178.162/eps/fin/papers/0312/0312009.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0312009.

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Length: 40 pages
Date of creation: 13 Dec 2003
Date of revision:
Handle: RePEc:wpa:wuwpfi:0312009

Note: Type of Document - pdf; prepared on Winxp; pages: 40; figures: some
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Web page: http://128.118.178.162

Related research

Keywords: Credit Risk; Credit Spread; Filtering Technique; Affine and Quadratic Models;

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References

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  1. Duffie, Darrell & Lando, David, 2001. "Term Structures of Credit Spreads with Incomplete Accounting Information," Econometrica, Econometric Society, vol. 69(3), pages 633-64, May.
  2. 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, vol. 10(2), pages 481-523.
  3. Tim Bollerslev & Jeffrey M. Wooldridge, 1988. "Quasi-Maximum Likelihood Estimation of Dynamic Models with Time-Varying Covariances," Working papers 505, Massachusetts Institute of Technology (MIT), Department of Economics.
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  8. Li Chen & Damir Filipovic, 2003. "A Simple Model for Credit Migration and Spread Curves," Finance 0305003, EconWPA.
  9. Delianedis, Gordon & Geske, Robert, 2001. "The Components of Corporate Credit Spreads: Default, Recovery, Tax, Jumps, Liquidity, and Market Factors," University of California at Los Angeles, Anderson Graduate School of Management qt32x284q3, Anderson Graduate School of Management, UCLA.
  10. Clark, Stephen A., 1993. "The valuation problem in arbitrage price theory," Journal of Mathematical Economics, Elsevier, vol. 22(5), pages 463-478.
  11. Markus Leippold & Liuren Wu, 2002. "Asset Pricing Under The Quadratic Class," Finance 0207015, EconWPA.
  12. 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.
  13. Markus Leippold & Liuren Wu, 2002. "Design and Estimation of Quadratic Term Structure Models," Finance 0207014, EconWPA.
  14. Jarrow, Robert A & Turnbull, Stuart M, 1995. " Pricing Derivatives on Financial Securities Subject to Credit Risk," Journal of Finance, American Finance Association, vol. 50(1), pages 53-85, March.
  15. Dong-Hyun Ahn & Robert F. Dittmar, 2002. "Quadratic Term Structure Models: Theory and Evidence," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 243-288, March.
  16. Li Chen & Damir Filipovic, 2003. "Credit Derivatives in an Affine Framework," Finance 0307002, EconWPA.
  17. Robert A. Jarrow & David Lando & Fan Yu, 2005. "Default Risk And Diversification: Theory And Empirical Implications," Mathematical Finance, Wiley Blackwell, vol. 15(1), pages 1-26.
  18. Li Chen & H. Vincent Poor, 2003. "Markovian Quadratic Term Structure Models For Risk-free And Defaultable Rates," Finance 0303008, EconWPA.
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