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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.

Suggested Citation

  • 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.).
  • Handle: RePEc:fip:fedgfe:2010-37
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    References listed on IDEAS

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    1. Michael B. Gordy & Sandeep Juneja, 2010. "Nested Simulation in Portfolio Risk Measurement," Management Science, INFORMS, vol. 56(10), pages 1833-1848, October.
    2. Gourieroux, C. & Laurent, J. P. & Scaillet, O., 2000. "Sensitivity analysis of Values at Risk," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 225-245, November.
    3. 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.
    4. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    5. 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.
    6. Gordy, Michael B., 2000. "A comparative anatomy of credit risk models," Journal of Banking & Finance, Elsevier, vol. 24(1-2), pages 119-149, January.
    7. 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.
    8. Nikola Tarashev & Claudio Borio & Kostas Tsatsaronis, 2010. "Attributing systemic risk to individual institutions," BIS Working Papers 308, Bank for International Settlements.
    9. 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.
    10. 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.
    11. 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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    Citations

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    Cited by:

    1. Serge Darolles & Christian Gouriéroux & Emmanuelle Jay, 2012. "Robust Portfolio Allocation with Systematic Risk Contribution Restrictions," Working Papers 2012-35, Center for Research in Economics and Statistics.
    2. repec:eee:jbfina:v:81:y:2017:i:c:p:105-113 is not listed on IDEAS
    3. Fermanian, Jean-David, 2014. "The limits of granularity adjustments," Journal of Banking & Finance, Elsevier, vol. 45(C), pages 9-25.
    4. Jean-David Fermanian, 2013. "The Limits of Granularity Adjustments," Working Papers 2013-27, Center for Research in Economics and Statistics.
    5. Avramidis, Panagiotis & Pasiouras, Fotios, 2015. "Calculating systemic risk capital: A factor model approach," Journal of Financial Stability, Elsevier, vol. 16(C), pages 138-150.
    6. Sofiya Avramova & Vanessa Le Leslé, 2012. "Revisiting Risk-Weighted Assets," IMF Working Papers 12/90, International Monetary Fund.
    7. 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.

    More about this item

    Keywords

    Risk management ; Econometric models;

    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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