Constructing the PD Term Structure

With the ongoing implementation of the IFRS 9 impairment framework increasing attention is paid to a consistent determination of expected credit lifetime losses. A clear distinction between point-in-time (PIT) and through-the-cycle (TTC) credit default probabilities is well known to be crucial for the construction of suitable PD term structures. However, due to typically insufficient data availability and quality the most widely spread approach to the PD term structure construction, i.e. the Exponentiation Approach, still relies on the exponentiation of observed one-year migration matrices irrespective of whether these are derived in a PIT- or TTC-context. In this paper the authors discuss the source of the conceptual inadequacy of this frequently used approach. Addressing these shortcomings, a new and conceptually consistent approach to deriving the genuine PD term structure is introduced and the fixation of its underlying model parameters is benchmarked on synthetic migration time series. This new method, which will be called Consistent Approach, allows in particular to estimate the dependence of the genuine PD term structure on the macroeconomic starting condition, rendering it applicable to both regulatory and internal stress testing. Finally, both the Exponentiation Approach and the Consistent Approach outlined in this paper are applied to actual migration data provided by GCD, the Global Credit Data consortium, allowing to observe the quantitative impact on PD term structure curves and thus on lifetime expected loss estimates. A profound impact on the term structure is found when comparing the market-standard Exponentiation Approach and the newly developed Consistent Approach.

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