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An axiomatic approach to default risk and model uncertainty in rating systems

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  • Max Nendel
  • Jan Streicher

Abstract

In this paper, we deal with an axiomatic approach to default risk. We introduce the notion of a default risk measure, which generalizes the classical probability of default (PD), and allows to incorporate model risk in various forms. We discuss different properties and representations of default risk measures via monetary risk measures, families of related tail risk measures, and Choquet capacities. In a second step, we turn our focus on default risk measures, which are given as worst-case PDs and distorted PDs. The latter are frequently used in order to take into account model risk for the computation of capital requirements through risk-weighted assets (RWAs), as demanded by the Capital Requirement Regulation (CRR). In this context, we discuss the impact of different default risk measures and margins of conservatism on the amount of risk-weighted assets.

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  • Max Nendel & Jan Streicher, 2023. "An axiomatic approach to default risk and model uncertainty in rating systems," Papers 2303.08217, arXiv.org, revised Sep 2023.
    • Handle: RePEc:arx:papers:2303.08217
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    References listed on IDEAS

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    1. Bellini, Fabio & Koch-Medina, Pablo & Munari, Cosimo & Svindland, Gregor, 2021. "Law-invariant functionals that collapse to the mean," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 83-91.
    2. Aouani, Zaier & Chateauneuf, Alain, 2008. "Exact capacities and star-shaped distorted probabilities," Mathematical Social Sciences, Elsevier, vol. 56(2), pages 185-194, September.
    3. Matteo Burzoni & Frank Riedel & H. Mete Soner, 2021. "Viability and Arbitrage Under Knightian Uncertainty," Econometrica, Econometric Society, vol. 89(3), pages 1207-1234, May.
    4. Patrick Beissner & Frank Riedel, 2019. "Equilibria Under Knightian Price Uncertainty," Econometrica, Econometric Society, vol. 87(1), pages 37-64, January.
    5. Fabio Maccheroni & Massimo Marinacci & Aldo Rustichini, 2006. "Ambiguity Aversion, Robustness, and the Variational Representation of Preferences," Econometrica, Econometric Society, vol. 74(6), pages 1447-1498, November.
    6. Erio Castagnoli & Fabio Maccheroni & Massimo Marinacci, 2004. "Choquet Insurance Pricing: A Caveat," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 481-485, July.
    7. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    8. Valeria Bignozzi & Matteo Burzoni & Cosimo Munari, 2020. "Risk Measures Based on Benchmark Loss Distributions," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 87(2), pages 437-475, June.
    9. Fabio Bellini & Pablo Koch-Medina & Cosimo Munari & Gregor Svindland, 2020. "Law-invariant functionals that collapse to the mean," Papers 2009.04144, arXiv.org, revised Jan 2021.
    10. Bruno Bouchard & Marcel Nutz, 2013. "Arbitrage and duality in nondominated discrete-time models," Papers 1305.6008, arXiv.org, revised Mar 2015.
    11. Nendel, Max & Riedel, Frank & Schmeck, Maren Diane, 2021. "A decomposition of general premium principles into risk and deviation," Insurance: Mathematics and Economics, Elsevier, vol. 100(C), pages 193-209.
    12. Burzoni, Matteo & Munari, Cosimo & Wang, Ruodu, 2022. "Adjusted Expected Shortfall," Journal of Banking & Finance, Elsevier, vol. 134(C).
    13. Wang, Shaun S. & Young, Virginia R. & Panjer, Harry H., 1997. "Axiomatic characterization of insurance prices," Insurance: Mathematics and Economics, Elsevier, vol. 21(2), pages 173-183, November.
    14. Felix-Benedikt Liebrich & Cosimo Munari, 2022. "Law-Invariant Functionals that Collapse to the Mean: Beyond Convexity," Mathematics and Financial Economics, Springer, volume 16, number 2, December.
    15. 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.
    16. repec:dau:papers:123456789/342 is not listed on IDEAS
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    Cited by:

    1. Corrado De Vecchi & Max Nendel & Jan Streicher, 2024. "Upper Comonotonicity and Risk Aggregation under Dependence Uncertainty," Papers 2406.19242, arXiv.org.

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