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Granularity Adjustment for Mark-to-Market Credit Risk Models

39 Pages Posted: 29 Jan 2011  

Michael B. Gordy

Board of Governors of the Federal Reserve

James V Marrone

University of Chicago

Multiple version iconThere are 2 versions of this paper

Date Written: January 28, 2011

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.

Keywords: Granularity adjustment, idiosyncratic risk, portfolio credit risk, value-at-risk, expected shortfall

JEL Classification: G17, G32

Suggested Citation

Gordy, Michael B. and Marrone, James V, Granularity Adjustment for Mark-to-Market Credit Risk Models (January 28, 2011). FEDS Working Paper No. 2010-37. Available at SSRN: https://ssrn.com/abstract=1750286 or http://dx.doi.org/10.2139/ssrn.1750286

Michael B. Gordy (Contact Author)

Board of Governors of the Federal Reserve ( email )

20th & C. St., N.W.
Washington, DC 20551
United States
202-452-3705 (Phone)

James V Marrone

University of Chicago ( email )

1126 E 59th St
Chicago, IL 60637
United States

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