CreditRisk+ by Fast Fourier Transform

Abstract

This paper focuses on the methodology described in CreditRisk+ Technical Document. Appendix A provides analytical explanations of the techniques used to generate the loss distribution arising from a credit portfolio. It is worth mentioning that although the underlying concepts are easy to grasp for those with an intermediate mathematical background, the notation used in this paper may bother those who are not fully familiar with it.

First, we concentrate on the concepts surrounding Probability Generating Functions and Convolution, and their application within CreditRisk+. Then, we explain, in practical terms, the use of the recurrence relation as used in CreditRisk+. Lastly, we develop an alternative way for calculating credit losses with CreditRisk+ via the Fast Fourier Transform (FFT). In order to close the gap between theory and practical implementation we provide VBA, MatLab and R codes that present step-by-step examples of practical applications.

Keywords: Fast Fourier Transform, Convolution, Credit Risk

JEL Classification: C00