# Infering the discounting rate for an illiquid company

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?

• Do you have observed yields for the company's traded debt? You could freeze their (average) spread over B. Dec 6, 2021 at 13:20
• No, I didn't specify it, but I'd like to focus on the case when there is no observable debt for the company and I only know the rating. I'll edit the answer to include this. Thanks!
– KT8
Dec 6, 2021 at 14:17
• In my opinion you must also consider the region.You may check other sources like markit. With that you can obtain either a proxy, or extrapolate a known region-sector-rating to yours. What I did in the past is to solve a binary correlation equation's system using dummy variables. Dec 6, 2021 at 14:38
• Could you suggest some reference where a solution that uses a binary correlation system is discussed?
– KT8
Dec 6, 2021 at 14:41
• You can do something like this: stackoverflow.com/questions/50733014/…. Dec 6, 2021 at 16:27