Journal of Risk Model Validation

Calibration of rating grades to point-in-time and through-the-cycle levels of probability of default

Mark Rubtsov

  • PD model calibration should occur at the rating grade level. This requires an adaptation of the classic ASRF model and introduces rating migration as a new element.
  • As a consequence, rating grade TTC PD becomes time-dependent. A link between rating migration and calibration levels provides a new definition of the rating function’s degree of PIT-ness.
  • The obtained closed-form solutions are flexible with respect to different rating practices (ie, rating based on forecast versus past financials) and explicitly account for the use of the business cycle forecast (as opposed to the actual realization). The ML estimation technique brings efficiency and offers a bridge to the regulatory margin of conservatism.
  • This technique enables banks to recalibrate their existing corporate rating systems to PIT and TTC levels, without the need to change their rating philosophy or to redefine the rating scale or to modify the existing rating function.  

The paper argues for the need for and importance of the dual calibration of a probability of default (PD) model (ie, calibration to both point-in-time (PIT) and through-the-cycle (TTC) PD levels). It explains why such a calibration should happen at the rating grade level, and how PD estimates can be assigned to a bank’s existing rating grades, ie, without introducing any changes to either the underlying (hybrid) rating function or the rating scale. This is done by first translating the traditional asymptotic single risk factor model underlying the Basel risk-weight formulas from its original obligor level to the rating grade level, and then determining the model’s parameters by using a maximum likelihood estimation. Standard deviations of the estimates obtained then provide a link to the regulatory margin of conservatism. Rating migration adds a new dimension to the model and leads to procyclical deviations of TTC PDs per grade from their long-term average counterparts. A link between rating migration and calibration levels gives a new definition to the rating function’s degree of PIT-ness, which becomes a key parameter responsible for the TTC stability at the portfolio level. The closed-form solutions obtained are flexible with respect to different patterns of rating migration and explicitly account for a prediction error in the business cycle model. The proposed technique is illustrated on a sample of corporate customers.

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