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Numerically stable computation of CreditRisk$$^+$$. (English) Zbl 1095.91032
Gundlach, Matthias (ed.) et al., CreditRisk$$^+$$ in the banking industry. Berlin: Springer (ISBN 3-540-20738-4/hbk). Springer Finance, 69-77 (2004).
Summary: We present an alternative numerical recursion scheme for CreditRisk$$^+$$, equivalent to an algorithm recently proposed by G. Giese [Enhancing CreditRisk$$^+$$. Risk 16, No. 4, 73–77 (2003)] based on well-known expansions of the logarithm and the exponential of a power series. We show that it is advantageous to the Panjer recursion advocated in the original CreditRisk$$^+$$ document, in that it is numerically stable. The crucial stability arguments are explained in detail. Furthermore, the computational complexity of the resulting algorithm is stated.
For the entire collection see [Zbl 1046.91001].

##### MSC:
 91B30 Risk theory, insurance (MSC2010) 91B28 Finance etc. (MSC2000)
##### Keywords:
Panjer recursion; complexity