By Calibration Type

Radius can build a wide variety of calibration solution types, under an extreme range of data conditions and business objectives. We discuss these ‘types’ here.

It is a common misconception that a model is ‘stuck’ with whatever calibration type is indicated by its intrinsic cycle signature. In other words, a model that does not fully capture the credit cycle through its information structure is not capable of (for example) generating PIT PDs.

However, this is actually not the case; there are a range of techniques that can be used to map a model’s outputs to the archetypal PIT or TTC patterns, and do this with stability and precision.

Obviously, it is easier to generate PIT PDs from a model that is already capturing a good proportion of the cycle. Likewise, it is easier to generate TTC PDs from a model that is unresponsive to the cycle.

Under the right conditions, we can build a calibration solution for a model that maps to the appropriate PIT signature (which is embodied by the credit cycle itself). Where these conditions cannot be met, there are modifications that can be made that still allow for the generation of PIT (or TTC) patterns, but the stability and precision of the solution may suffer. These methodology extensions can be configured to create a quantifiable margin-of-conservatism, increasing the utility and acceptability of the solution.

The “right conditions” are, in highly-simplified terms, reasonably logical:

  • Enough historical default data to cover a full cycle (and preferably more than one)
  • Ideally, a reasonable panel of historical model output data (i.e. forecast default rates), to match against observed default rates, although this is not absolutely required
  • A model with stable predictive power, under a range of conditions, that ‘responds well’ to the cycle
  • A relatively large, homogenous portfolio in terms of the number of borrowers, without excessive concentrations

These solutions are necessarily more complex than a standard Base calibration and almost always involve an iterative scheme of some description. In plain terms, an “iterative scheme” implies an ongoing, periodic modelling exercise or algorithm and any calibration solution of this type would set this scheme out, in depth.

By Portfolio Type

Over the years, we have performed calibrations for every virtually portfolio type there is, from retail portfolios where the number of defaults is large, to low default portfolios (LDPs) where the paucity of default data creates significant challenges for parameter estimation. In fact, we have considerable experience with LDPs — both model build and calibration — primarily in Tier 1, AIRB environments.

For calibration, it’s not so much what the notional portfolio type is; that’s obviously just a label. What matters far more are things like:

  • the complexity of the calibration objectives (i.e. the desired calibration type);
  • the portfolio’s composition through time;
  • the portfolio’s internal homogeneity;
  • the nature of the associated credit cycle; and
  • the fundamental resources available for parameter estimation (volume of historical default events, availability of benchmarks, etc).


In reality, ‘portfolio type’ is just a convenient handle for recurring patterns within the attributes above.