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Structured Dictionary Learning of Rating Migration Matrices for Credit Risk Modeling

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  • Michaël Allouche

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Emmanuel Gobet

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Clara Lage

    (CMAP - Centre de Mathématiques Appliquées de l'Ecole polytechnique - Inria - Institut National de Recherche en Informatique et en Automatique - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique)

  • Edwin Mangin

    (BNPP)

Abstract

Rating Migration Matrix is a crux to assess credit risks. Modeling and predicting these matrices are then an issue of great importance for risk managers in any financial institution. As a challenger to usual parametric modeling approaches, we propose a new structured dictionary learning model with auto-regressive regularization that is able to meet key expectations and constraints: small amount of data, fast evolution in time of these matrices, economic interpretability of the calibrated model. To show the model applicability, we present a numerical test with real data. The source code and the data are available at https://github.com/michael-allouche/ dictionary-learning-RMM.git for the sake of reproducibility of our research.

Suggested Citation

  • Michaël Allouche & Emmanuel Gobet & Clara Lage & Edwin Mangin, 2024. "Structured Dictionary Learning of Rating Migration Matrices for Credit Risk Modeling," Post-Print hal-03715954, HAL.
    • Handle: RePEc:hal:journl:hal-03715954
    DOI: 10.1007/s00180-023-01449-y
    Note: View the original document on HAL open archive server: https://hal.science/hal-03715954v2
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    References listed on IDEAS

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    1. Gondzio, Jacek, 2012. "Interior point methods 25 years later," European Journal of Operational Research, Elsevier, vol. 218(3), pages 587-601.
    2. Florian Bourgey & Emmanuel Gobet & Clément Rey, 2020. "Meta-model of a large credit risk portfolio in the Gaussian copula model," Post-Print hal-02291548, HAL.
    3. Klaus Neusser, 2016. "Time Series Econometrics," Springer Texts in Business and Economics, Springer, number 978-3-319-32862-1, January.
    4. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    5. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
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