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A Discrete-Time Approach to Arbitrage-Free Pricing of Credit Derivatives

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  • Sanjiv Ranjan Das

    (Harvard University & NBER, Graduate School of Business, Boston, Massachusetts 02163)

  • Rangarajan K. Sundaram

    (New York University, Stern School of Business, New York, New York 10012)

Abstract

This paper develops a framework for modelling risky debt and valuing credit derivatives that is flexible and simple to implement, and that is, to the maximum extent possible, based on observables. Our approach is based on expanding the Heath-Jarrow-Morton term-structure model to allow for defaultable debt. Rather than follow the procedure of implying out the behavior of spreads from assumptions concerning the default process, we work directly with the evolution of spreads. The risk-neutral drifts in the resulting model possess a recursive representation that facilitates implementation and makes it possible to handle path-dependence and early exercise features without difficulty. The framework permits embedding a variety of specifications for default; we present an empirical example of a default structure which provides promising calibration results.

Suggested Citation

  • Sanjiv Ranjan Das & Rangarajan K. Sundaram, 2000. "A Discrete-Time Approach to Arbitrage-Free Pricing of Credit Derivatives," Management Science, INFORMS, vol. 46(1), pages 46-62, January.
    • Handle: RePEc:inm:ormnsc:v:46:y:2000:i:1:p:46-62
    DOI: 10.1287/mnsc.46.1.46.15124
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    References listed on IDEAS

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    Cited by:

    1. Masakazu Miura & Kenichiro Tamaki & Takayuki Shiohama, 2013. "Asymptotic Expansion for Term Structures of Defaultable Bonds with Non-Gaussian Dependent Innovations," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(4), pages 311-344, November.
    2. Gady Jacoby & Chuan Liao & Jonathan A. Batten, 2007. "A Pure Test for the Elasticity of Yield Spreads," The Institute for International Integration Studies Discussion Paper Series iiisdp195, IIIS.
    3. Francis A. Longstaff & Sanjay Mithal & Eric Neis, 2005. "Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit Default Swap Market," Journal of Finance, American Finance Association, vol. 60(5), pages 2213-2253, October.
    4. Francois, Pascal & Hubner, Georges, 2004. "Credit derivatives with multiple debt issues," Journal of Banking & Finance, Elsevier, vol. 28(5), pages 997-1021, May.
    5. John Kiff & François-Louis Michaud & Janet Mitchell, 2003. "An Analytical Review of Credit Risk Transfer Instruments," Financial Stability Review, National Bank of Belgium, vol. 1(1), pages 125-150, June.
    6. Frank X. Zhang, 2003. "What did the credit market expect of Argentina default? Evidence from default swap data," Finance and Economics Discussion Series 2003-25, Board of Governors of the Federal Reserve System (U.S.).
    7. Didier Cossin & Tomas Hricko & Daniel Aunon-Nerin & Zhijiang Huang, 2002. "Exploring for the Determinants of Credit Risk in Credit Default Swap Transaction Data: Is Fixed-Income Markets’ Information Suffcient to Evaluate Credit Risk?," FAME Research Paper Series rp65, International Center for Financial Asset Management and Engineering.
    8. Joachim Inkmann & David Blake & Zhen Shi, 2017. "Managing Financially Distressed Pension Plans In The Interest Of Beneficiaries," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 84(2), pages 539-565, June.
    9. Houweling, Patrick & Vorst, Ton, 2005. "Pricing default swaps: Empirical evidence," Journal of International Money and Finance, Elsevier, vol. 24(8), pages 1200-1225, December.
    10. Pourkhanali, Armin & Kim, Jong-Min & Tafakori, Laleh & Fard, Farzad Alavi, 2016. "Measuring systemic risk using vine-copula," Economic Modelling, Elsevier, vol. 53(C), pages 63-74.
    11. Rong Huang & Xintian Lin & Yuan Xie, 2023. "Does CDS market price intangible asset value? Evidence from SG&A expenditure," Review of Quantitative Finance and Accounting, Springer, vol. 61(2), pages 701-728, August.
    12. Augusto Castillo, 2004. "Firm and Corporate Bond Valuation: A Simulation Dynamic Programming Approach," Latin American Journal of Economics-formerly Cuadernos de Economía, Instituto de Economía. Pontificia Universidad Católica de Chile., vol. 41(124), pages 345-360.
    13. Longstaff, Francis A. & Mithal, Sanjay & Neis, Eric, 2004. "Corporate Yield Spreads: Default Risk or Liquidity? New Evidence from the Credit-Default Swap Market, previously titled: "The Credit-Default Swap Market: Is Credit Protection Priced Correctly?&qu," University of California at Los Angeles, Anderson Graduate School of Management qt8gn7h03k, Anderson Graduate School of Management, UCLA.
    14. Chiarella, Carl & Fanelli, Viviana & Musti, Silvana, 2011. "Modelling the evolution of credit spreads using the Cox process within the HJM framework: A CDS option pricing model," European Journal of Operational Research, Elsevier, vol. 208(2), pages 95-108, January.
    15. Chuang-Chang Chang & Ruey-Jenn Ho & Chengfew Lee, 2010. "Pricing credit card loans with default risks: a discrete-time approach," Review of Quantitative Finance and Accounting, Springer, vol. 34(4), pages 413-438, May.
    16. Acharya, Viral & Bharath, Sreedhar T & Srinivasan, Anand, 2003. "Understanding the Recovery Rates on Defaulted Securities," CEPR Discussion Papers 4098, C.E.P.R. Discussion Papers.
    17. Haibin Zhu, 2006. "An Empirical Comparison of Credit Spreads between the Bond Market and the Credit Default Swap Market," Journal of Financial Services Research, Springer;Western Finance Association, vol. 29(3), pages 211-235, June.
    18. Michael Adler & Jeong Song, 2010. "The behavior of emerging market sovereigns' credit default swap premiums and bond yield spreads," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 15(1), pages 31-58.
    19. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    20. Sanjiv R. Das & Rangarajan K. Sundaram, 2007. "An Integrated Model for Hybrid Securities," Management Science, INFORMS, vol. 53(9), pages 1439-1451, September.
    21. Viviana Fanelli & Silvana Musti, 2007. "Pricing of CDS Options with the HJM approach: a Numerical Implementation," Quaderni DSEMS 26-2007, Dipartimento di Scienze Economiche, Matematiche e Statistiche, Universita' di Foggia.
    22. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    23. Antionio Diaz & Frank Skinner, 2001. "Estimating Corporate Yield Curves," ICMA Centre Discussion Papers in Finance icma-dp2001-01, Henley Business School, University of Reading.

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