# Are there any well known methods of testing through-the-cycle rating systems?

Rating systems, as defined by the Basel II Accord, can be classified into two broad types - through-the-cycle (TTC) or point-in-time (PIT) - and the probability of default predicted by such a system can usually have different interpretations. In practice, no rating system is purely TTC or PIT.

One advantage of PIT systems are that they are easy to 'backtest' - if the PIT system predicts the 1 year probability of default, we can always "score" the obligors using the system 1 year back, and then compare the actual default rates against the predicted probability of default.

Since TTC systems predict the probability of default over different economic cycles, it is hard to backtest such a system as the realized default rates may not match with the probability depending on where we are in the economic cycle.

I am having a hard time finding any existing research or literature on this topic. Most of them mention the standard measures like ROC, Gini, Accuracy Ratio, etc. which tells us whether the rating system can sufficiently differentiate the likelihood of default. However, this does not say if the probabilities output by the rating system make sense.

Can anyone point me out to any relevant research, books or documents which may help?

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I think the national regulators are more concerned with downturn LGD (sort of TTC LGD) rather than a TTC PD. Therefore most rating systems which I encounter are closer to being PIT and thereby easier to validate using the techniques you mentioned and also to backtest.

But in any case, model validation is a very subjective field despite the various quantitative tools that exist and the expert judgement of the analyst must come through.

Anyway, some of the best research on model validation remains as follows:

http://www.bis.org/publ/bcbs_wp14.htm

http://www.risk.net/digital_assets/5028/jrm_v1n1a4.pdf

I will add more references as I track their urls ;)

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Thanks - upvoted, but I personally do not see downturn LGD as a TTC measure. A TTC PD can go below the actual default rate in downturn conditions - in that case, capital goes down but your expected loss goes up assuming it is calculated using a PIT PD. In my experience, downturn LGD is always higher than realized LGD. I think the reasoning is that while PD is automatically 'stressed' using the regulatory capital formula, such is not the case with EAD or LGD - hence we use downturn estimates. – Mozan Sykol Jan 30 '13 at 16:45