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Modelling Rating Transitions

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  • Weißbach, Rafael
  • Mollenhauer, Thomas

Abstract

The time-continuous discrete-state Markov process is a model for rating transitions. One parameter, namely the intensity to migrate to an adjacent rating state, implies an ordinal rating to have an intuitive metric. State-specific intensities generalize the state-stationarity. Observing Markov processes from a multiplicative intensity model, the maximum likelihood parameter estimators for both models can be written as a martingale transform of the processes that count transitions between the rating states. A Taylor expansion reveals consistency and asymptotic normality of the parameter estimates, resulting in a chi-square-distributed likelihood ratio of state-stationarity and the state-specific model. This extents to time-stationarity. Simulations contrast the asymptotic results with finite samples. An application to a sufficiently large set of credit rating histories shows that the one-parameter model can be a good starting point.

Suggested Citation

  • Weißbach, Rafael & Mollenhauer, Thomas, 2011. "Modelling Rating Transitions," VfS Annual Conference 2011 (Frankfurt, Main): The Order of the World Economy - Lessons from the Crisis 48698, Verein für Socialpolitik / German Economic Association.
    • Handle: RePEc:zbw:vfsc11:48698
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    References listed on IDEAS

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    1. Koopman, Siem Jan & Lucas, André, 2008. "A Non-Gaussian Panel Time Series Model for Estimating and Decomposing Default Risk," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 510-525.
    2. 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 449-470, May.
    3. Kiefer, Nicholas M. & Larson, C. Erik, 2007. "A simulation estimator for testing the time homogeneity of credit rating transitions," Journal of Empirical Finance, Elsevier, vol. 14(5), pages 818-835, December.
    4. Weißbach, Rafael & Walter, Ronja, 2010. "A likelihood ratio test for stationarity of rating transitions," Journal of Econometrics, Elsevier, vol. 155(2), pages 188-194, April.
    5. Frydman, Halina & Schuermann, Til, 2008. "Credit rating dynamics and Markov mixture models," Journal of Banking & Finance, Elsevier, vol. 32(6), pages 1062-1075, June.
    6. Bangia, Anil & Diebold, Francis X. & Kronimus, Andre & Schagen, Christian & Schuermann, Til, 2002. "Ratings migration and the business cycle, with application to credit portfolio stress testing," Journal of Banking & Finance, Elsevier, vol. 26(2-3), pages 445-474, March.
    7. Kiefer, Nicholas M., 2010. "Default Estimation and Expert Information," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 320-328.
    8. Rafael Weißbach & Patrick Tschiersch & Claudia Lawrenz, 2009. "Testing time-homogeneity of rating transitions after origination of debt," Empirical Economics, Springer, vol. 36(3), pages 575-596, June.
    9. 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.
    10. 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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    Citations

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    Cited by:

    1. Guglielmo D’Amico, 2015. "Rate of Occurrence of Failures (ROCOF) of Higher-Order for Markov Processes: Analysis, Inference and Application to Financial Credit Ratings," Methodology and Computing in Applied Probability, Springer, vol. 17(4), pages 929-949, December.
    2. Benjamin Strohner & Rafael Weißbach, 2016. "Altersspezifische Querschnittsanalyse der Fertilität in Mecklenburg-Vorpommern mit dem EM-Algorithmus [Age-Specific Cross-Sectional Analysis of the Fertility in Mecklenburg-West Pomerania with the ," AStA Wirtschafts- und Sozialstatistisches Archiv, Springer;Deutsche Statistische Gesellschaft - German Statistical Society, vol. 10(4), pages 269-288, December.
    3. Rafael Weißbach & Wladislaw Poniatowski & Walter Krämer, 2013. "Nearest neighbor hazard estimation with left-truncated duration data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 33-47, January.
    4. 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.
    5. 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.

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    More about this item

    Keywords

    Rating; Metricality; Multiple Markov process; Counting process; Likelihood ratio;
    All these keywords.

    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C41 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Duration Analysis; Optimal Timing Strategies
    • G33 - Financial Economics - - Corporate Finance and Governance - - - Bankruptcy; Liquidation

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