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# bootstrap estimates for a transistion matrix, was: migration probabilities using cohort approach

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12-07-2017 12:06 AM - last edited on 12-09-2017 03:23 PM by mkeintz

Hello,

I am trying to determine estimates of migration probabilities using the cohort approach.

Here is the code I have so far to get the transition probabilities matrix and I would like some help in determining the probabilities of default for credit ratings.

Code:

Proc freq data = ratingdata;

Tables rating2015_B*Rating2015_E

/nopercent norow nocol;

Title ‘transition matrix’;

Run;

Here is the matrix:

Here is the credit rating dataset that I have attached.

thank you!

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Posted in reply to Anna7

12-08-2017 04:31 PM

I take it that rating D is for default, since you only have a D column, but no D row. So if you want probabilities, rerun the PROC FREQ, but eliminate the "norow" option. Down the column D you'll see the probability of default, for each row.

Of course one of your problems is that the normal ascii sort sequence won't put your rating codes in order according the intended credit worthiness. Yes, the A's precede B's precede C's, but within A, they are not ordered as a credit analyst would want. Why do I bring this up? Because you might want to develop cumulative probabilities from the high credit score, including progressively weaker credit ratings. To see what I mean run

```
proc freq data = ratingdata;
tables rating2015_e rating2015_B
/nopercent norow cumcol;
title ‘transition matrix’;
run;
```

Note I changed rating2015_b from the row variables to the column variable. This made using the "cumcol" option useful (there is no cumrow option). Of course, this would be much better if proc freq would order by actual credit worthiness.

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Posted in reply to mkeintz

12-08-2017 05:05 PM

Thank you for your help. After that, I am trying to determine specifically:

using nonparametric bootstrap method (exclude the defaults) to generate 95% confidence intervals for default rates of each rating category.

Explore the relationship between the length of CIs and number of bootstrap samples and confidence level.

Do you have any idea how to proceed with this? I am a newbie with SAS, so I am unaware of how to code this and what functions I can use?

Thank you.