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The limits of granularity adjustments

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  • Fermanian, Jean-David

Abstract

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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    Cited by:

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    2. Greig Smith & Goncalo dos Reis, 2017. "Robust and Consistent Estimation of Generators in Credit Risk," Papers 1702.08867, arXiv.org, revised Oct 2017.
    3. 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.

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    More about this item

    Keywords

    Credit portfolio model; Granularity adjustment; Value-at-risk; Fourier Transform; G32; G17;
    All these keywords.

    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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