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# 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

expand 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

```