Wavelet analysis of business cycles for validation of probability of default: what is the influence of the current credit crisis on model validation?

Marco J. van der Burgt

Abstract

ABSTRACT

According to Basel II, the probability of default (PD) should be a longterm average of one-year default rates. In this paper, long term is interpreted as one business cycle. When the PD is compared with the actual observed default rates in the PD rating validation process, two questions are relevant: how long is a business cycle and where are we in the business cycle? We present two techniques in order to address these questions: Fourier analysis and wavelet analysis. The analysis of default rates in the period 1981-2007 from Standard & Poor's reveals two business cycles of 10.67 years.