A methodology for point-in-time–through-the-cycle probability of default decomposition in risk classification systems

Using a Merton model framework (consistent with Basel II formulas), we develop a methodology for point-in-time (PIT) and through-the-cycle (TTC) probability of default (PD) decomposition in credit risk classification systems, primarily for corporates. Such a methodology is important for reducing the procyclicality of the capital requirement. We mathematically define the degree of PIT of a rating model and the state of the economic cycle. Simple analytical expressions for full PIT PD and TTC PD are derived, which allow easy implementation of the methodology in a bank's IT system. Furthermore, we discuss different methods for estimation of parameters as well as possible implications for risk adjusted profitability and steering.