Numerically Stable Computation of CreditRisk+

by Hermann Haaf of Commerzbank AG,
Oliver Reiß of IKB Deutsche Industriebank AG, and
John Schoenmakers of the Weierstrass Institute

Summer 2004

Abstract: The CreditRisk+ model launched by Credit Suisse First Boston in 1997 is widely used by practitioners in the banking sector as a simple means for the quantification of credit risk, primarily of the loan book. We present an alternative numerical recursion scheme for CreditRisk+, equivalent to an algorithm recently proposed by Giese (*) , that is based on well-known expansions of the logarithm and the exponential of a power series. We show that it is advantageous for the Panjer recursion advocated in the original CreditRisk+ document, in that it is numerically stable. The crucial stability arguments are explained in detail. We explain how to apply the suggested recursion scheme to incorporate stochastic exposures into the CreditRisk+ model as introduced by Tasche (2004). Finally, the computational complexity of the resulting algorithm is stated and compared with other methods for computing the CreditRisk+ loss distribution.

AMS Classification: 91B30, 60-08, 60E10.

Keywords: Credit risk, Probability generating function, Computation of functions of power series, Numerical stability.

Published in: Journal of Risk, Vol. 6, No. 4, (Summer 2004), pp. 1-10.

(*) G. Giese, Enhancing CreditRisk+, Risk, Vol. 16, No. 4, pp. 73-77, 2003.

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