Calculating Credit Risk Capital Charges with the One-factor Model

by Susanne Emmer of Dr. Nagler & Company GmbH, and
Dirk Tasche of Deutsche Bundesbank

January 4, 2005

Abstract: Even in the simple one-factor credit portfolio model that underlies the Basel II regulatory capital rules coming into force in 2007, the exact contributions to credit value-at-risk can only be calculated with Monte-Carlo simulation or with approximation algorithms that often involve numerical integration. As this may require a lot of computational time, there is a need for approximate analytical formulae. In this note, we develop formulae according to two different approaches: the granularity adjustment approach initiated by M.Gordy and T.Wilde, and a semi-asymptotic approach. The application of the formulae is illustrated with a numerical example.

Keywords: One-factor model, capital charge, granularity adjustment, quantile derivative.

Published in: Journal of Risk, Vol. 7, No. 2, (Winter 2005), pp. 85-101.

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