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Multiple Ratings Model of Defaultable Term Structure

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  • Tomasz R. Bielecki
  • Marek Rutkowski

Abstract

A new approach to modeling credit risk, to valuation of defaultable debt and to pricing of credit derivatives is developed. Our approach, based on the Heath, Jarrow, and Morton (1992) methodology, uses the available information about the credit spreads combined with the available information about the recovery rates to model the intensities of credit migrations between various credit ratings classes. This results in a conditionally Markovian model of credit risk. We then combine our model of credit risk with a model of interest rate risk in order to derive an arbitrage‐free model of defaultable bonds. As expected, the market price processes of interest rate risk and credit risk provide a natural connection between the actual and the martingale probabilities.

Suggested Citation

  • Tomasz R. Bielecki & Marek Rutkowski, 2000. "Multiple Ratings Model of Defaultable Term Structure," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 125-139, April.
    • Handle: RePEc:bla:mathfi:v:10:y:2000:i:2:p:125-139
    DOI: 10.1111/1467-9965.00085
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    Citations

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    Cited by:

    1. Alain Monfort & Jean-Paul Renne, 2013. "Default, Liquidity, and Crises: an Econometric Framework," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 11(2), pages 221-262, March.
    2. Batten, Jonathan & Hogan, Warren, 2002. "A perspective on credit derivatives," International Review of Financial Analysis, Elsevier, vol. 11(3), pages 251-278.
    3. Chang, Charles & Fuh, Cheng-Der & Kao, Chu-Lan Michael, 2017. "Reading between the ratings: Modeling residual credit risk and yield overlap," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 114-135.
    4. Das, Sanjiv Ranjan & Acharya, Viral & Sundaram, Rangarajan K, 2002. "Pricing Credit Derivatives with Rating Transitions," CEPR Discussion Papers 3329, C.E.P.R. Discussion Papers.
    5. Kevin Kamm & Michelle Muniz, 2022. "A novel approach to rating transition modelling via Machine Learning and SDEs on Lie groups," Papers 2205.15699, arXiv.org.
    6. Stephen Zamore & Kwame Ohene Djan & Ilan Alon & Bersant Hobdari, 2018. "Credit Risk Research: Review and Agenda," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 54(4), pages 811-835, March.
    7. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," 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 20, pages 1207-1246, Elsevier.
    8. Fanelli, Viviana, 2017. "Implications of implicit credit spread volatilities on interest rate modelling," European Journal of Operational Research, Elsevier, vol. 263(2), pages 707-718.
    9. Fanelli, Viviana, 2016. "A defaultable HJM modelling of the Libor rate for pricing Basis Swaps after the credit crunch," European Journal of Operational Research, Elsevier, vol. 249(1), pages 238-244.
    10. repec:wyi:journl:002109 is not listed on IDEAS
    11. Martino Grasselli & Giulio Miglietta, 2016. "A flexible spot multiple-curve model," Quantitative Finance, Taylor & Francis Journals, vol. 16(10), pages 1465-1477, October.
    12. Wei, Jason Z., 2003. "A multi-factor, credit migration model for sovereign and corporate debts," Journal of International Money and Finance, Elsevier, vol. 22(5), pages 709-735, October.
    13. Bielecki, Tomasz R. & Jakubowski, Jacek & Niewęgłowski, Mariusz, 2017. "Conditional Markov chains: Properties, construction and structured dependence," Stochastic Processes and their Applications, Elsevier, vol. 127(4), pages 1125-1170.

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