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Calculating credit risk capital charges with the one-factor model

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  • Susanne Emmer
  • Dirk Tasche

Abstract

Even in the simple one-factor credit portfolio model that underlies the Basel II regulatory capital rules coming into force in 2007, the exact contributions to credit value-at-risk can only be calculated with Monte-Carlo simulation or with approximation algorithms that often involve numerical integration. As this may require a lot of computational time, there is a need for approximate analytical formulae. In this note, we develop formulae according to two different approaches: the granularity adjustment approach initiated by M. Gordy and T. Wilde, and a semi-asymptotic approach. The application of the formulae is illustrated with a numerical example. Keywords: One-factor model, capital charge, granularity adjustment, quantile derivative.

Suggested Citation

  • Susanne Emmer & Dirk Tasche, 2003. "Calculating credit risk capital charges with the one-factor model," Papers cond-mat/0302402, arXiv.org, revised Jan 2005.
  • Handle: RePEc:arx:papers:cond-mat/0302402
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    References listed on IDEAS

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    1. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    2. Carlo Acerbi & Dirk Tasche, 2002. "Expected Shortfall: A Natural Coherent Alternative to Value at Risk," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 31(2), pages 379-388, July.
    3. Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, vol. 12(3), pages 199-232, July.
    4. Carlo Acerbi & Dirk Tasche, 2001. "Expected Shortfall: a natural coherent alternative to Value at Risk," Papers cond-mat/0105191, arXiv.org.
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    Cited by:

    1. Puzanova, Natalia & Düllmann, Klaus, 2013. "Systemic risk contributions: A credit portfolio approach," Journal of Banking & Finance, Elsevier, vol. 37(4), pages 1243-1257.
    2. Marc Busse & Michel Dacorogna & Marie Kratz, 2014. "The Impact of Systemic Risk on the Diversification Benefits of a Risk Portfolio," Risks, MDPI, Open Access Journal, vol. 2(3), pages 1-17, July.
    3. Jean-David Fermanian, 2013. "The Limits of Granularity Adjustments," Working Papers 2013-27, Center for Research in Economics and Statistics.
    4. Pierpaolo Grippa & Lucyna Gornicka, 2016. "Measuring Concentration Risk - A Partial Portfolio Approach," IMF Working Papers 16/158, International Monetary Fund.
    5. Nikola A. Tarashev & Haibin Zhu, 2007. "Modelling and calibration errors in measures of portfolio credit risk," BIS Working Papers 230, Bank for International Settlements.
    6. Gordy, Michael B. & Marrone, James, 2012. "Granularity adjustment for mark-to-market credit risk models," Journal of Banking & Finance, Elsevier, vol. 36(7), pages 1896-1910.
    7. Bernardi, Enrico & Falangi, Federico & Romagnoli, Silvia, 2015. "A hierarchical copula-based world-wide valuation of sovereign risk," Insurance: Mathematics and Economics, Elsevier, vol. 61(C), pages 155-169.
    8. Sylvia Gottschalk, 2016. "Entropy and credit risk in highly correlated markets," Papers 1604.07042, arXiv.org.
    9. Fermanian, Jean-David, 2014. "The limits of granularity adjustments," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 9-25.
    10. Rosen, Dan & Saunders, David, 2010. "Risk factor contributions in portfolio credit risk models," Journal of Banking & Finance, Elsevier, vol. 34(2), pages 336-349, February.
    11. Dirk Tasche, 2005. "Measuring sectoral diversification in an asymptotic multi-factor framework," Papers physics/0505142, arXiv.org, revised Jul 2006.
    12. Morone, Marco & Cornaglia, Anna & Mignola, Giulio, 2012. "Determining marginal contributions of the economic capital of credit risk portfolio: an analytical approach," MPRA Paper 39119, University Library of Munich, Germany.
    13. Avramidis, Panagiotis & Pasiouras, Fotios, 2015. "Calculating systemic risk capital: A factor model approach," Journal of Financial Stability, Elsevier, vol. 16(C), pages 138-150.
    14. Dirk Tasche, 2003. "A traffic lights approach to PD validation," Papers cond-mat/0305038, arXiv.org.
    15. Kim, Joocheol & Lee, Duyeol, 2007. "Simulation based approach for measuring concentration risk," MPRA Paper 2968, University Library of Munich, Germany, revised 19 Apr 2007.
    16. M. B. Gordy & E. Lutkebohmert, 2013. "Granularity Adjustment for Regulatory Capital Assessment," International Journal of Central Banking, International Journal of Central Banking, vol. 9(3), pages 38-77, September.
    17. Gottschalk, Sylvia, 2017. "Entropy measure of credit risk in highly correlated markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 478(C), pages 11-19.
    18. Nikola Tarashev & Haibin Zhu, 2007. "Measuring portfolio credit risk: modelling versus calibration errors," BIS Quarterly Review, Bank for International Settlements, March.
    19. Susanne Emmer & Marie Kratz & Dirk Tasche, 2013. "What is the best risk measure in practice? A comparison of standard measures," Papers 1312.1645, arXiv.org, revised Apr 2015.
    20. Bernardi Enrico & Romagnoli Silvia, 2015. "A copula-based hierarchical hybrid loss distribution," Statistics & Risk Modeling, De Gruyter, vol. 32(1), pages 73-87, April.
    21. Nikola Tarashev & Haibin Zhu, 2008. "Specification and Calibration Errors in Measures of Portfolio Credit Risk: The Case of the ASRF Model," International Journal of Central Banking, International Journal of Central Banking, vol. 4(2), pages 129-173, June.
    22. Gürtler, Marc & Hibbeln, Martin & Vöhringer, Clemens, 2007. "Measuring concentration risk for regulatory purposes," Working Papers IF26V4, Technische Universität Braunschweig, Institute of Finance.

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