Numerically Stable Computation of CreditRisk+
by Hermann Haaf of Commerzbank AG,
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.
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.