Let's say I would like to determine the incremental discounting rate (e.g. as in IFRS-16) for a company $X$ with a rating score of $Y$ and belonging to a sector $Z$. Usually, any data provider such as Bloomberg and Reuters only displays the yields or CDS spreads for some of the sectors and only for liquid ratings: That is, even if the sector $Z$ appears in the Bloomberg/Reuters list, I would only be able to find these rates for ratings all the way down to $BB$ usually, and sometimes even for a $B$ score.
The question is the following: If company $X$ has a $CCC$ rating and I only know the yields of the companies of that sector down to a $BB$ (or $B$) rating, how could I infer the yield for such a company? Is there any reference you know where this is treated that you can recommend? I'm also assuming the absence of traded or observable debt for the company.
A naive approach would be to use a linear extrapolation down to $CCC$, by notching. However, we know that yields are non-linear in rating, so that could only be used as a dummy extrapolation. I have also seen some DNN/multifactor regressions, but since it's always difficult to harvest data for those kind of companies it feels a bit unnatural to train a DNN on $\left\lbrace AAA, B \right\rbrace$ data, and then use it to price debt on a $CCC$-rated company.
I would like to use another idea for that extrapolation (something a bit more rigorous would be ideal). The question is which one, and do you know any reference that supports that assumption?