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The limits of granularity adjustments


  • Fermanian, Jean-David


We provide a rigorous proof of granularity adjustment (GA) formulas to evaluate loss distributions and risk measures (value-at-risk) in the case of heterogenous portfolios, multiple systematic factors and random recoveries. As a significant improvement with respect to the literature, we detail all the technical conditions of validity and provide an upper bound of the remainder term for finite portfolio sizes. Moreover, we deal explicitly with the case of general loss distributions, possibly with masses. For some simple portfolio models, we prove empirically that the granularity adjustments do not always improve the infinitely granular first-order approximations. This stresses the importance of checking some conditions of regularity before relying on such techniques. Smoothing the underlying loss distributions through random recoveries or exposures improves the GA performances in general.

Suggested Citation

  • Fermanian, Jean-David, 2014. "The limits of granularity adjustments," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 9-25.
  • Handle: RePEc:eee:jbfina:v:45:y:2014:i:c:p:9-25 DOI: 10.1016/j.jbankfin.2014.04.023

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    References listed on IDEAS

    1. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    2. Acerbi, Carlo & Tasche, Dirk, 2002. "On the coherence of expected shortfall," Journal of Banking & Finance, Elsevier, vol. 26(7), pages 1487-1503, July.
    3. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
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    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. Edward I. Altman & Brooks Brady & Andrea Resti & Andrea Sironi, 2005. "The Link between Default and Recovery Rates: Theory, Empirical Evidence, and Implications," The Journal of Business, University of Chicago Press, vol. 78(6), pages 2203-2228, November.
    8. 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.
    9. Susanne Emmer & Dirk Tasche, 2003. "Calculating credit risk capital charges with the one-factor model," Papers cond-mat/0302402,, revised Jan 2005.
    10. Patrick Gagliardini & Christian Gouriéroux, 2011. "Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 9(2), pages 237-280, Spring.
    11. Mikhail Voropaev, 2009. "Analytical Framework for Credit Portfolios. Part I: Systematic Risk," Papers 0911.0223,, revised Jul 2011.
    12. Con Keating & Hyun Song Shin & Charles Goodhart & Jon Danielsson, 2001. "An Academic Response to Basel II," FMG Special Papers sp130, Financial Markets Group.
    13. Salah Amraoui & Laurent Cousot & Sebastien Hitier & Jean-Paul Laurent, 2012. "Pricing CDOs with state-dependent stochastic recovery rates," Quantitative Finance, Taylor & Francis Journals, vol. 12(8), pages 1219-1240, February.
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    Cited by:

    1. Greig Smith & Goncalo dos Reis, 2017. "Robust and Consistent Estimation of Generators in Credit Risk," Papers 1702.08867,, revised Oct 2017.
    2. 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.

    More about this item


    Credit portfolio model; Granularity adjustment; Value-at-risk; Fourier Transform; G32; G17;

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation


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