Fourier Inversion Techniques for CreditRisk+

The CreditRisk+ model is described in terms of characteristic functions, and two methods to determine the distribution of the credit loss based on Fourier inversion are presented. For the convenience of the reader, a short introduction to the theory of characteristic functions and the Fourier transformation is given. Then two general results are stated how to obtain the distribution of a random variable from its characteristic function. These general techniques, which are based on Fourier inversion, will be applied to the CreditRisk+ model and yield efficient and numerically stable algorithms, which provide the loss distribution in the CreditRisk+ framework. Advantages of this approach are that the algorithms are easy to implement and that a basic loss unit is not required.