# transprobtothresholds

Convert from transition probabilities to credit quality thresholds

## Syntax

`thresh = transprobtothresholds(trans)`

## Description

`thresh = transprobtothresholds(trans)` transforms transition probabilities into credit quality thresholds.

## Input Arguments

 `trans` `M`-by-`N` matrix with transition probabilities, in percent. Entries cannot be negative and cannot exceed 100, and all rows must add up to 100. Any given row in the `M`-by-`N` input matrix `trans` determines a probability distribution over a discrete set of `N` ratings. If the ratings are `'R1'`,`...`,`'RN'`, then for any row i `trans`(`i`,`j`) is the probability of migrating into `'Rj'`. If `trans` is a standard transition matrix, then `M` ≦ `N` and row i contains the transition probabilities for issuers with rating `'Ri'`. But `trans` does not have to be a standard transition matrix. `trans` can contain individual transition probabilities for a set of `M`-specific issuers, with `M` > `N`. The credit quality thresholds `thresh`(i,j) are critical values of a standard normal distribution z, such that:```trans(i,N) = P[z < thresh(i,N)], trans(i,j) = P[z < thresh(i,j)] - P[z < thresh(i,j+1)], for 1<=j

## Output Arguments

 `thresh` `M`-by-`N` matrix of credit quality thresholds.

## Examples

collapse all

### Transform Transition Probabilities Into Credit Quality Thresholds

Use historical credit rating input data from `Data_TransProb.mat`. Load input data from file `Data_TransProb.mat`.

```load Data_TransProb % Estimate transition probabilities with default settings transMat = transprob(data) ```
```transMat = Columns 1 through 7 93.1170 5.8428 0.8232 0.1763 0.0376 0.0012 0.0001 1.6166 93.1518 4.3632 0.6602 0.1626 0.0055 0.0004 0.1237 2.9003 92.2197 4.0756 0.5365 0.0661 0.0028 0.0236 0.2312 5.0059 90.1846 3.7979 0.4733 0.0642 0.0216 0.1134 0.6357 5.7960 88.9866 3.4497 0.2919 0.0010 0.0062 0.1081 0.8697 7.3366 86.7215 2.5169 0.0002 0.0011 0.0120 0.2582 1.4294 4.2898 81.2927 0 0 0 0 0 0 0 Column 8 0.0017 0.0396 0.0753 0.2193 0.7050 2.4399 12.7167 100.0000 ```

Obtain the credit quality thresholds.

```thresh = transprobtothresholds(transMat) ```
```thresh = Columns 1 through 7 Inf -1.4846 -2.3115 -2.8523 -3.3480 -4.0083 -4.1276 Inf 2.1403 -1.6228 -2.3788 -2.8655 -3.3166 -3.3523 Inf 3.0264 1.8773 -1.6690 -2.4673 -2.9800 -3.1631 Inf 3.4963 2.8009 1.6201 -1.6897 -2.4291 -2.7663 Inf 3.5195 2.9999 2.4225 1.5089 -1.7010 -2.3275 Inf 4.2696 3.8015 3.0477 2.3320 1.3838 -1.6491 Inf 4.6241 4.2097 3.6472 2.7803 2.1199 1.5556 Inf Inf Inf Inf Inf Inf Inf Column 8 -4.1413 -3.3554 -3.1736 -2.8490 -2.4547 -1.9703 -1.1399 Inf ```

## References

Gupton, G. M., C. C. Finger, and M. Bhatia, CreditMetrics, Technical Document, RiskMetrics Group, Inc., 2007.