# PD validation in the low/no default setting

The topic of this question is the validation as prescribed in the Basel N ($N \ge 2$) framework. The task is given the probability of default $p_k$ for $K$ rating classes at time $t$ and the outcome on a credit portfolio at time $t+1$ to judge the quality (discriminatory power, calibration) of the rating model.

In practice there are cirumstances where the task of validation is difficult: We can face the situation where we have a low number of creditors (due to a special segment or because the bank just entered the market). Furthermore we can have no defaults at all. This is either by pure chance (for example in a small portfolio) or because the portfolio bears low risk.

It appears that Dirk Tasche wrote some papers in this setting and he and his collaborators are most often cited. I somehow can't see the connection to validation. But isn't there more literature?

Some literature deals with calibrating models but what is best practice in validation of no default portfolios? I would be interested in retail and corporate portfolios. I appreciate any remarks. Maybe you can help me find more or apply Tasche's findings to validation.