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1

I would think it is because it can be bound between 2 points it can assume wide range shapes It fits the data empirically (as you said) On a related note Sometime back I read a paper which might give you more formal reason. It is for estimating and simulating recovery rates . I havnt used it to model credit migration probabilities . But I think one ...

4

Actually, there is a practical way to do it. You can use you PoD estimates to assign a credit rating to your securities and then use a published transition matrix for your purposes. Or you can estimate transition probabilities by linear interpolation based on the PoD values that you have. Here is a publication containing transition matrices from ...

5

You cannot do it. It is an under-determined problem. That is to say, a whole multitude (subspace of $\mathbb{R}^{N\times N}$) of migration matrices will agree with any given table of default probabilities. Say you want to find a transition matrix for 2 states (IG, HY) plus default \left(\begin{matrix} p_{11} & p_{12} & p_{1D} \\ p_{21} ...

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