IDEAS home Printed from https://ideas.repec.org/p/arx/papers/cond-mat-0302402.html
   My bibliography  Save this paper

Calculating credit risk capital charges with the one-factor model

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/cond-mat/0302402
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Rosen, Dan & Saunders, David, 2009. "Analytical methods for hedging systematic credit risk with linear factor portfolios," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 37-52, January.
    2. Yu Takata, 2018. "Application of Granularity Adjustment Approximation Method to Incremental Value-at-Risk in Concentrated Portfolios," Economics Bulletin, AccessEcon, vol. 38(4), pages 2320-2330.
    3. García-Céspedes, Rubén & Moreno, Manuel, 2017. "An approximate multi-period Vasicek credit risk model," Journal of Banking & Finance, Elsevier, vol. 81(C), pages 105-113.
    4. Laurent, Jean-Paul & Sestier, Michael & Thomas, Stéphane, 2016. "Trading book and credit risk: How fundamental is the Basel review?," Journal of Banking & Finance, Elsevier, vol. 73(C), pages 211-223.
    5. Gürtler, Marc & Hibbeln, Martin & Vöhringer, Clemens, 2007. "Measuring concentration risk for regulatory purposes," Working Papers IF26V4, Technische Universität Braunschweig, Institute of Finance.
    6. Yi-Ping Chang & Jing-Xiu Lin & Chih-Tun Yu, 2016. "Calculating Value-at-Risk Using the Granularity Adjustment Method in the Portfolio Credit Risk Model with Random Loss Given Default," Journal of Economics and Management, College of Business, Feng Chia University, Taiwan, vol. 12(2), pages 157-176, August.
    7. Fermanian, Jean-David, 2014. "The limits of granularity adjustments," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 9-25.
    8. Jean-David Fermanian, 2013. "The Limits of Granularity Adjustments," Working Papers 2013-27, Center for Research in Economics and Statistics.
    9. Rubén García-Céspedes & Manuel Moreno, 2020. "Random LGD adjustments in the Vasicek credit risk model," The European Journal of Finance, Taylor & Francis Journals, vol. 26(18), pages 1856-1875, December.
    10. Uberti, Pierpaolo & Figini, Silvia, 2010. "How to measure single-name credit risk concentrations," European Journal of Operational Research, Elsevier, vol. 202(1), pages 232-238, April.
    11. Kao, Lie-Jane, 2015. "A portfolio-invariant capital allocation scheme penalizing concentration risk," Economic Modelling, Elsevier, vol. 51(C), pages 560-570.
    12. Klaus Düllmann & Nancy Masschelein, 2006. "Sector Concentration in Loan Portfolios and Economic Capital," Working Paper Research 105, National Bank of Belgium.
    13. Vilislav Boutchaktchiev, 2025. "Inferred Loss Rate as a Credit Risk Measure in the Bulgarian Banking System," Mathematics, MDPI, vol. 13(9), pages 1-18, April.
    14. Richard Gerlach & Antonio Naimoli & Giuseppe Storti, 2025. "Using quantile time series and historical simulation to forecast financial risk multiple steps ahead," Papers 2502.20978, arXiv.org, revised Mar 2025.
    15. 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.
    16. Avramidis, Panagiotis & Pasiouras, Fotios, 2015. "Calculating systemic risk capital: A factor model approach," Journal of Financial Stability, Elsevier, vol. 16(C), pages 138-150.
    17. Masschelein, Nancy & Düllmann, Klaus, 2006. "Sector concentration in loan portfolios and economic capital," Discussion Paper Series 2: Banking and Financial Studies 2006,09, Deutsche Bundesbank.
    18. 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.
    19. Osmundsen, Kjartan Kloster, 2017. "Using Expected Shortfall for Credit Risk Regulation," UiS Working Papers in Economics and Finance 2017/4, University of Stavanger.
    20. 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.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:cond-mat/0302402. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.