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Efficient estimation of transition rates between credit ratings from observations at discrete time points

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  • Mogens Bladt
  • Michael SØrensen

Abstract

The paper demonstrates how discrete time credit rating data (e.g. annual observations) can be analysed by means of a continuous-time Markov model. Two methods for estimating the transition intensities are given: the EM algorithm and an MCMC approach. The estimated transition intensities can be used to estimate the matrix of probabilities of transitions between all credit ratings, including default probabilities, over any time horizon. Thus the advantages of a continuous-time model can be obtained without continuous-time data. Estimates of the variance of estimators as well as confidence and credibility intervals are presented, and a test for equality of two intensity matrices is proposed. The methods are demonstrated by analysis of a large data set drawn from Moody's Corporate Bond Default Database, where reasonable estimates are obtained from annual observations.

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  • Mogens Bladt & Michael SØrensen, 2009. "Efficient estimation of transition rates between credit ratings from observations at discrete time points," Quantitative Finance, Taylor & Francis Journals, vol. 9(2), pages 147-160.
    • Handle: RePEc:taf:quantf:v:9:y:2009:i:2:p:147-160
    DOI: 10.1080/14697680802624948
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    References listed on IDEAS

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    1. D. Oakes, 1999. "Direct calculation of the information matrix via the EM," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(2), pages 479-482, April.
    2. Robert A. Jarrow & David Lando & Stuart M. Turnbull, 2008. "A Markov Model for the Term Structure of Credit Risk Spreads," World Scientific Book Chapters, in: Financial Derivatives Pricing Selected Works of Robert Jarrow, chapter 18, pages 411-453, World Scientific Publishing Co. Pte. Ltd..
    3. Mogens Bladt & Michael Sørensen, 2005. "Statistical inference for discretely observed Markov jump processes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(3), pages 395-410, June.
    4. Lando, David & Skodeberg, Torben M., 2002. "Analyzing rating transitions and rating drift with continuous observations," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 423-444, March.
    5. Christensen, Jens H.E. & Hansen, Ernst & Lando, David, 2004. "Confidence sets for continuous-time rating transition probabilities," Journal of Banking & Finance, Elsevier, vol. 28(11), pages 2575-2602, November.
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    Cited by:

    1. Linda Möstel & Marius Pfeuffer & Matthias Fischer, 2020. "Statistical inference for Markov chains with applications to credit risk," Computational Statistics, Springer, vol. 35(4), pages 1659-1684, December.
    2. Tamás Kristóf, 2021. "Sovereign Default Forecasting in the Era of the COVID-19 Crisis," JRFM, MDPI, vol. 14(10), pages 1-24, October.
    3. Lapshin, Viktor & Anton, Markov, 2022. "MCMC-based credit rating aggregation algorithm to tackle data insufficiency," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 68, pages 50-72.
    4. Xiaofeng Nie & Tamer Boyacı & Mehmet Gümüş & Saibal Ray & Dan Zhang, 2017. "Joint procurement and demand-side bidding strategies under price volatility," Annals of Operations Research, Springer, vol. 257(1), pages 121-165, October.
    5. Voß, Sebastian & Weißbach, Rafael, 2014. "A score-test on measurement errors in rating transition times," Journal of Econometrics, Elsevier, vol. 180(1), pages 16-29.
    6. Alexander Kremer & Rafael Weißbach, 2013. "Consistent estimation for discretely observed Markov jump processes with an absorbing state," Statistical Papers, Springer, vol. 54(4), pages 993-1007, November.
    7. Greig Smith & Goncalo dos Reis, 2017. "Robust and Consistent Estimation of Generators in Credit Risk," Papers 1702.08867, arXiv.org, revised Oct 2017.
    8. Marius Pfeuffer & Goncalo dos Reis & Greig smith, 2018. "Capturing Model Risk and Rating Momentum in the Estimation of Probabilities of Default and Credit Rating Migrations," Papers 1809.09889, arXiv.org, revised Feb 2020.
    9. Kremer, Alexander & Weißbach, Rafael, 2014. "Asymptotic normality for discretely observed Markov jump processes with an absorbing state," Statistics & Probability Letters, Elsevier, vol. 90(C), pages 136-139.
    10. David Azriel & Paul D. Feigin & Avishai Mandelbaum, 2019. "Erlang-S: A Data-Based Model of Servers in Queueing Networks," Management Science, INFORMS, vol. 65(10), pages 4607-4635, October.

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