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Paris-Princeton Lectures on Mathematical Finance 2004
Paris-Princeton Lectures on Mathematical Finance 2004 Finance 2004

by Rene A. Carmona, Ivar Ekeland, Arturo Kohatsu-Higa, Jean-Michel Lasry, Pierre-Louis Lions, Huyen Pham, Erik Taflin, Springer, (
October 1, 2007), Paperback, 248 pages

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The Mathematics of Credit Derivatives: The Essential Credit Modelling and Pricing Companion
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In Rememberance: World Trade Center (WTC)

A Risk-Factor Model Foundation for Ratings-Based Bank Capital Rules

by Michael B. Gordy of the Board of Governors of the Federal Reserve System

October 22, 2002

Abstract: When economic capital is calculated using a portfolio model of credit value-at-risk, the marginal capital requirement for an instrument depends, in general, on the properties of the portfolio in which it is held. By contrast, ratings-based capital rules, including both the current Basel Accord and its proposed revision, assign a capital charge to an instrument based only on its own characteristics. I demonstrate that ratings-based capital rules can be reconciled with the general class of credit VaR models. Contributions to VaR are portfolio-invariant only if (a) there is only a single systematic risk factor driving correlations across obligors, and (b) no exposure in a portfolio accounts for more than an arbitrarily small share of total exposure. Analysis of rates of convergence to asymptotic VaR leads to a simple and accurate portfolio-level add-on charge for undiversified idiosyncratic risk. There is no similarly simple way to address violation of the single factor assumption.

JEL Classification: G31, G38.

Published in: Journal of Financial Intermediation, Vol. 12, No. 3, (July 2003), pp. 199-232.

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