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Wavelet Analysis of Business Cycles for Validation of Probability of Default: What is the influence of the current credit crisis on model validation?

by Marco van der Burgt of Atradius N.V.

January 2009

Abstract: According to Basel II, the Probability of Default (PD) should be a long-term average of 1-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 & Poors reveals two business cycles of 10.67 years.

JEL Classification: G1, G11.

Keywords: Business cycles, wavelets, Fourier analysis, validation.

Published in: Journal of Risk Model Validation, Vol. 3, No. 1, (Spring 2009).

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