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Pricing Credit Derivatives with Rating Transitions

  • Acharya, Viral V
  • Das, Sanjiv Ranjan
  • Sundaram, Rangarajan K

We develop a model for pricing risky debt and valuing credit derivatives that is easily calibrated to existing variables. Our approach is based on expanding the Heath-Jarrow-Morton (1990) term-structure model and its extension, the Das-Sundaram (2000) model to allow for defaultable debt with rating transitions. The framework has two salient features, comprising extensions over the earlier work: (i) it employs a rating transition matrix as the driver for the default process, and (ii) the entire set of rating categories is calibrated jointly, allowing, with minimal assumptions, arbitrage-free restrictions across rating classes, as a bond migrates amongst them. We provide an illustration of the approach by applying it to price credit sensitive notes that have coupon payments that are linked to the rating of the underlying credit.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 3329.

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Date of creation: Apr 2002
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Handle: RePEc:cpr:ceprdp:3329
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  1. 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.
  2. Philipp J. Schonbucher, 1997. "Team Structure Modelling of Defaultable Bonds," FMG Discussion Papers dp272, Financial Markets Group.
  3. Duffie, Darrell & Huang, Ming, 1996. " Swap Rates and Credit Quality," Journal of Finance, American Finance Association, vol. 51(3), pages 921-49, July.
  4. Tomasz R. Bielecki & Marek Rutkowski, 2000. "Multiple Ratings Model of Defaultable Term Structure," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 125-139.
  5. Masaaki Kijima, 1998. "Monotonicities in a Markov Chain Model for Valuing Corporate Bonds Subject to Credit Risk," Mathematical Finance, Wiley Blackwell, vol. 8(3), pages 229-247.
  6. Gregory R. Duffee, 1998. "The Relation Between Treasury Yields and Corporate Bond Yield Spreads," Journal of Finance, American Finance Association, vol. 53(6), pages 2225-2241, December.
  7. 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 637-54, May-June.
  8. 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 351-67, May.
  9. 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.
  10. 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 449-70, May.
  11. In Joon Kim & Krishna Ramaswamy & Suresh Sundaresan, 1993. "Does Default Risk in Coupons Affect the Valuation of Corporate Bonds?: A Contingent Claims Model," Financial Management, Financial Management Association, vol. 22(3), Fall.
  12. Geske, Robert, 1977. "The Valuation of Corporate Liabilities as Compound Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 541-552, November.
  13. In Joon Kim & Krishna Ramaswamy & Suresh Sundaresan, . "The Valuation of Corporate Fixed Income Securities," Rodney L. White Center for Financial Research Working Papers 32-89, Wharton School Rodney L. White Center for Financial Research.
  14. Heath, David & Jarrow, Robert & Morton, Andrew, 1990. "Bond Pricing and the Term Structure of Interest Rates: A Discrete Time Approximation," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(04), pages 419-440, December.
  15. Delianedis, Gordon & Geske, Robert, 1998. "Credit Risk and Risk Neutral Default Probabilities: Information About Migrations and Defaults," University of California at Los Angeles, Anderson Graduate School of Management qt7dm2d31p, Anderson Graduate School of Management, UCLA.
  16. Mason, Scott P. & Bhattacharya, Sudipto, 1981. "Risky debt, jump processes, and safety covenants," Journal of Financial Economics, Elsevier, vol. 9(3), pages 281-307, September.
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  18. Hayne E. Leland., 1994. "Corporate Debt Value, Bond Covenants, and Optimal Capital Structure," Research Program in Finance Working Papers RPF-233, University of California at Berkeley.
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