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The Limits of Granularity Adjustments

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  • Jean-David Fermanian

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    (CREST (ENSAE))

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    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 at a finite distance. 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

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    Bibliographic Info

    Paper provided by Centre de Recherche en Economie et Statistique in its series Working Papers with number 2013-27.

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    Length: 50
    Date of creation: Dec 2013
    Date of revision:
    Handle: RePEc:crs:wpaper:2013-27

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    Related research

    Keywords: Credit portfolio model; Granularity adjustment; Value-at-risk; Fourier Transform;

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    References

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    1. C. Gourieroux & J.P. Laurent & O. Scaillet, 2000. "Sensitivity analysis of values at risk," THEMA Working Papers 2000-04, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
    2. Michael B. Gordy & James Marrone, 2010. "Granularity adjustment for mark-to-market credit risk models," Finance and Economics Discussion Series 2010-37, Board of Governors of the Federal Reserve System (U.S.).
    3. 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.
    4. Michael B. Gordy, 1998. "A comparative anatomy of credit risk models," Finance and Economics Discussion Series 1998-47, Board of Governors of the Federal Reserve System (U.S.).
    5. Patrick GAGLIARDINI & Christian GOURIEROUX, 2010. "Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk," Working Papers 2010-07, Centre de Recherche en Economie et Statistique.
    6. Susanne Emmer & Dirk Tasche, 2003. "Calculating credit risk capital charges with the one-factor model," Papers cond-mat/0302402, arXiv.org, revised Jan 2005.
    7. 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.
    8. 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.
    9. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers 2000-05, Centre de Recherche en Economie et Statistique.
    10. Hui Chen & Scott Joslin, 2011. "Generalized Transform Analysis of Affine Processes and Applications in Finance," NBER Working Papers 16906, National Bureau of Economic Research, Inc.
    11. Carlo Acerbi & Dirk Tasche, 2001. "On the coherence of Expected Shortfall," Papers cond-mat/0104295, arXiv.org, revised May 2002.
    12. 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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