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Robust and consistent estimation of generators in credit risk

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  • G. dos Reis
  • G. Smith

Abstract

Bond rating Transition Probability Matrices (TPMs) are built over a one-year time-frame and for many practical purposes, like the assessment of risk in portfolios or the computation of banking Capital Requirements (e.g. the new IFRS 9 regulation), one needs to compute the TPM and probabilities of default over a smaller time interval. In the context of continuous time Markov chains (CTMC) several deterministic and statistical algorithms have been proposed to estimate the generator matrix. We focus on the Expectation-Maximization (EM) algorithm by Bladt and Sorensen. [J. R. Stat. Soc. Ser. B (Stat. Method.), 2005, 67, 395–410] for a CTMC with an absorbing state for such estimation. This work’s contribution is threefold. Firstly, we provide directly computable closed form expressions for quantities appearing in the EM algorithm and associated information matrix, allowing to easy approximation of confidence intervals. Previously, these quantities had to be estimated numerically and considerable computational speedups have been gained. Secondly, we prove convergence to a single set of parameters under very weak conditions (for the TPM problem). Finally, we provide a numerical benchmark of our results against other known algorithms, in particular, on several problems related to credit risk. The EM algorithm we propose, padded with the new formulas (and error criteria), outperforms other known algorithms in several metrics, in particular, with much less overestimation of probabilities of default in higher ratings than other statistical algorithms.

Suggested Citation

  • G. dos Reis & G. Smith, 2018. "Robust and consistent estimation of generators in credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 18(6), pages 983-1001, June.
  • Handle: RePEc:taf:quantf:v:18:y:2018:i:6:p:983-1001
    DOI: 10.1080/14697688.2017.1383627
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    Citations

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    Cited by:

    1. Rebeca Peláez & Ricardo Cao & Juan M. Vilar, 2022. "Bootstrap Bandwidth Selection and Confidence Regions for Double Smoothed Default Probability Estimation," Mathematics, MDPI, vol. 10(9), pages 1-25, May.
    2. Alan Riva-Palacio & Ramsés H. Mena & Stephen G. Walker, 2023. "On the estimation of partially observed continuous-time Markov chains," Computational Statistics, Springer, vol. 38(3), pages 1357-1389, September.
    3. 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.
    4. Tamás Kristóf, 2021. "Sovereign Default Forecasting in the Era of the COVID-19 Crisis," JRFM, MDPI, vol. 14(10), pages 1-24, October.
    5. 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.
    6. Oliver Blümke, 2022. "Multiperiod default probability forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(4), pages 677-696, July.
    7. 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.

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