On probability of default and its relation to observed default frequency and a common factor

This paper considers a definition of through-the-cycle (TTC) as independent from an economic state that can result in a time-varying TTC probability of default (PD). A top-down approach is proposed to transform hybrid PDs into TTC PDs through the use of a point-in-time-ness (PITness) parameter as an additional parameter to the Vasicek model, which expresses the dependency of a hybrid PD on a common factor. The proposed framework aims to explain fluctuations in observed default frequency (ODF) and modeled default frequency time series. A novel approach is considered that defines ODF as analogous to an aggregated PIT PD stemming from a perfect foresight model, which is not available to the modeler but can be assumed backward in time for calibration purposes. An elaborate segmentation framework is considered to understand differences in both the Vasicek correlation and the PITness parameter for a portfolio of obligors; this can be applied to both retail and nonretail portfolios.