Through-the-cycle to Point-in-time Probabilities of Default Conversion: Inconsistencies in the Vasicek Approach

Abstract

While regulators generate and advocate the use of through the cycle (TtC) probabilities of default (PDs) for regulatory capital calculations, accounting standards (such as IFRs9) require organisations to use point in time (PiT) PDs. TtC PDs are based on long-term average conditions and do not adequately capture current credit risk conditions, underestimating credit losses during economic downturns or periods of financial stress. PiT PDs reflect the specific risk conditions prevailing at a given moment in time and provide a more granular assessment of credit risk. While many techniques measure PiT PDs directly, mathematical approaches also exist which convert TtC PDs into PiT PDs. PiT PDs are also routinely forecasted, projected into the future to allow estimation of the present value of future possible credit-related losses. Vasicek’s (1987) model is in common use for this purpose. Using a stylistic range of possible input values for Vasicek’s model, loan credit quality is found to be differentially affected (improving for some and deteriorating for others) for some of these values. This is counterintuitive and reflects a functional flaw in the model.