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Granularity adjustment for mark-to-market credit risk models

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  • Michael B. Gordy
  • James Marrone

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 with respect to model parameters in CreditMetrics reveal striking and counterintuitive patterns. We explain these relationships with a stylized model of portfolio risk.

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Bibliographic Info

Paper provided by Board of Governors of the Federal Reserve System (U.S.) in its series Finance and Economics Discussion Series with number 2010-37.

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Date of creation: 2010
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Handle: RePEc:fip:fedgfe:2010-37

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Keywords: Risk management ; Econometric models;

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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. 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. Gourieroux, C. & Jasiak, J., 2012. "Granularity adjustment for default risk factor model with cohorts," Journal of Banking & Finance, Elsevier, vol. 36(5), pages 1464-1477.
  4. 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.
  5. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
  6. 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, vol. 26(7), pages 1317-1334, July.
  7. repec:fth:inseep:2000-05 is not listed on IDEAS
  8. Altman, Edward I. & Rijken, Herbert A., 2004. "How rating agencies achieve rating stability," Journal of Banking & Finance, Elsevier, vol. 28(11), pages 2679-2714, November.
  9. 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.
  10. Nikola Tarashev & Claudio Borio & Kostas Tsatsaronis, 2010. "Attributing systemic risk to individual institutions," BIS Working Papers 308, Bank for International Settlements.
  11. 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.).
  12. Susanne Emmer & Dirk Tasche, 2003. "Calculating credit risk capital charges with the one-factor model," Papers cond-mat/0302402, arXiv.org, revised Jan 2005.
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Cited by:
  1. Jean-David Fermanian, 2013. "The Limits of Granularity Adjustments," Working Papers 2013-27, Centre de Recherche en Economie et Statistique.
  2. Serge Darolles & Christian Gouriéroux & Emmanuelle Jay, 2012. "Robust Portfolio Allocation with Systematic Risk Contribution Restrictions," Working Papers 2012-35, 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, vol. 9(3), pages 38-77, September.

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