Quantifying model risk within a CreditRisk+ framework

Matthias Fischer and Alexander Mertel

Abstract

ABSTRACT

In order to quantify an aspect of model risk in CreditRisk+, the assumption of gamma-distributed sectors is omitted by introducing a more flexible family of distributions: tempered stable distributions. The theoretical results are applied to the original Credit Suisse Financial Products framework and to the common background vector model recently launched by Fischer and Dietz. In order to calculate the loss distribution, a short review of the Panjer recursion is given and, in accordance with Gerhold et al, an extension that guarantees numerical stability in cases where the recursion might fail is presented. In addition to the distribution of the portfolio loss, contributions to value-at-risk are calculated as well, using the nested evaluation algorithm of Haaf et al. Finally, some empirical results on risk figures and risk contributions for a benchmark portfolio are given, emphasizing the effects of heavy-tailedness of the sector distributions.