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Regulatory Capital Modeling For Credit Risk

Author

Listed:
  • MAREK RUTKOWSKI

    (School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia)

  • SILVIO TARCA

    (School of Mathematics and Statistics, F07, University of Sydney, NSW 2006, Australia)

Abstract

The Basel II internal ratings-based (IRB) approach to capital adequacy for credit risk plays an important role in protecting the banking sector against insolvency. We outline the mathematical foundations of regulatory capital for credit risk, and extend the model specification of the IRB approach to a more general setting than the usual Gaussian case. It rests on the proposition that quantiles of the distribution of conditional expectation of portfolio percentage loss may be substituted for quantiles of the portfolio loss distribution. We present a more compact proof of this proposition under weaker assumptions. Then, constructing a portfolio that is representative of credit exposures of the Australian banking sector, we measure the rate of convergence, in terms of number of obligors, of empirical loss distributions to the asymptotic (infinitely fine-grained) portfolio loss distribution. Moreover, we evaluate the sensitivity of credit risk capital to dependence structure as modeled by asset correlations and elliptical copulas. Access to internal bank data collected by the prudential regulator distinguishes our research from other empirical studies on the IRB approach.

Suggested Citation

  • Marek Rutkowski & Silvio Tarca, 2015. "Regulatory Capital Modeling For Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-44.
    • Handle: RePEc:wsi:ijtafx:v:18:y:2015:i:05:n:s021902491550034x
    DOI: 10.1142/S021902491550034X
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    Citations

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    Cited by:

    1. Metzler A., 2020. "State dependent correlations in the Vasicek default model," Dependence Modeling, De Gruyter, vol. 8(1), pages 298-329, January.
    2. Metzler A., 2020. "State dependent correlations in the Vasicek default model," Dependence Modeling, De Gruyter, vol. 8(1), pages 298-329, January.
    3. Greig Smith & Goncalo dos Reis, 2017. "Robust and Consistent Estimation of Generators in Credit Risk," Papers 1702.08867, arXiv.org, revised Oct 2017.
    4. Huang, Zhenzhen & Kwok, Yue Kuen & Xu, Ziqing, 2024. "Efficient algorithms for calculating risk measures and risk contributions in copula credit risk models," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 132-150.
    5. Leitao, Álvaro & Ortiz-Gracia, Luis, 2020. "Model-free computation of risk contributions in credit portfolios," Applied Mathematics and Computation, Elsevier, vol. 382(C).

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