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Granularity adjustment for mark-to-market credit risk models

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  • Gordy, Michael B.
  • Marrone, James

Abstract

The impact of undiversified idiosyncratic risk on value-at-risk and expected shortfall can be approximated analytically via a methodology known as granularity adjustment (GA). In principle, the GA methodology can be applied to any risk-factor model of portfolio risk. Thus far, however, analytical results have been derived only for simple models of actuarial loss, i.e., credit loss due to default. We demonstrate that the GA is entirely tractable for single-factor versions of a large class of models that includes all the commonly used mark-to-market approaches. Our approach covers both finite ratings-based models and models with a continuum of obligor states. We apply our methodology to CreditMetrics and KMV Portfolio Manager, as these are benchmark models for the finite and continuous classes, respectively. Comparative statics of the GA reveal striking and counterintuitive patterns. We explain these relationships with a stylized model of portfolio risk.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Banking & Finance.

Volume (Year): 36 (2012)
Issue (Month): 7 ()
Pages: 1896-1910

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Handle: RePEc:eee:jbfina:v:36:y:2012:i:7:p:1896-1910

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Web page: http://www.elsevier.com/locate/jbf

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Keywords: Granularity adjustment; Idiosyncratic risk; Portfolio credit risk; Value-at-risk; Expected shortfall;

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References

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  1. Susanne Emmer & Dirk Tasche, 2003. "Calculating credit risk capital charges with the one-factor model," Papers cond-mat/0302402, arXiv.org, revised Jan 2005.
  2. Merton, Robert C., 1973. "On the pricing of corporate debt: the risk structure of interest rates," Working papers 684-73., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  3. Michael B. Gordy & Sandeep Juneja, 2008. "Nested simulation in portfolio risk measurement," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 2008-21, Board of Governors of the Federal Reserve System (U.S.).
  4. Christian Gourieroux & J. P. Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Econometric Society World Congress 2000 Contributed Papers 0162, Econometric Society.
  5. Patrick GAGLIARDINI & Christian GOURIEROUX, 2010. "Approximate Derivative Pricing for Large Classes of Homogeneous Assets with Systematic Risk," Working Papers, Centre de Recherche en Economie et Statistique 2010-07, Centre de Recherche en Economie et Statistique.
  6. Michael B. Gordy, 1998. "A comparative anatomy of credit risk models," Finance and Economics Discussion Series, Board of Governors of the Federal Reserve System (U.S.) 1998-47, Board of Governors of the Federal Reserve System (U.S.).
  7. Altman, Edward I. & Rijken, Herbert A., 2004. "How rating agencies achieve rating stability," Journal of Banking & Finance, Elsevier, Elsevier, vol. 28(11), pages 2679-2714, November.
  8. Gordy, Michael B., 2003. "A risk-factor model foundation for ratings-based bank capital rules," Journal of Financial Intermediation, Elsevier, Elsevier, vol. 12(3), pages 199-232, July.
  9. Christian Gourieroux & Jean-Paul Laurent & Olivier Scaillet, 2000. "Sensitivity Analysis of Values at Risk," Working Papers, Centre de Recherche en Economie et Statistique 2000-05, Centre de Recherche en Economie et Statistique.
  10. Gourieroux, C. & Jasiak, J., 2012. "Granularity adjustment for default risk factor model with cohorts," Journal of Banking & Finance, Elsevier, Elsevier, vol. 36(5), pages 1464-1477.
  11. Nikola Tarashev & Claudio Borio & Kostas Tsatsaronis, 2010. "Attributing systemic risk to individual institutions," BIS Working Papers 308, Bank for International Settlements.
  12. Frey, Rudiger & McNeil, Alexander J., 2002. "VaR and expected shortfall in portfolios of dependent credit risks: Conceptual and practical insights," Journal of Banking & Finance, Elsevier, Elsevier, vol. 26(7), pages 1317-1334, July.
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Cited by:
  1. Serge Darolles & Christian Gouriéroux & Emmanuelle Jay, 2012. "Robust Portfolio Allocation with Systematic Risk Contribution Restrictions," Working Papers, Centre de Recherche en Economie et Statistique 2012-35, Centre de Recherche en Economie et Statistique.
  2. Jean-David Fermanian, 2013. "The Limits of Granularity Adjustments," Working Papers, Centre de Recherche en Economie et Statistique 2013-27, Centre de Recherche en Economie et Statistique.
  3. M. B. Gordy & E. Lutkebohmert, 2013. "Granularity Adjustment for Regulatory Capital Assessment," International Journal of Central Banking, International Journal of Central Banking, International Journal of Central Banking, vol. 9(3), pages 38-77, September.

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