transprobtothresholds
Convert from transition probabilities to credit quality thresholds
Description
Examples
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 = 8×8
93.1170 5.8428 0.8232 0.1763 0.0376 0.0012 0.0001 0.0017
1.6166 93.1518 4.3632 0.6602 0.1626 0.0055 0.0004 0.0396
0.1237 2.9003 92.2197 4.0756 0.5365 0.0661 0.0028 0.0753
0.0236 0.2312 5.0059 90.1846 3.7979 0.4733 0.0642 0.2193
0.0216 0.1134 0.6357 5.7960 88.9866 3.4497 0.2919 0.7050
0.0010 0.0062 0.1081 0.8697 7.3366 86.7215 2.5169 2.4399
0.0002 0.0011 0.0120 0.2582 1.4294 4.2898 81.2927 12.7167
0 0 0 0 0 0 0 100.0000
Obtain the credit quality thresholds.
thresh = transprobtothresholds(transMat)
thresh = 8×8
Inf -1.4846 -2.3115 -2.8523 -3.3480 -4.0083 -4.1276 -4.1413
Inf 2.1403 -1.6228 -2.3788 -2.8655 -3.3166 -3.3523 -3.3554
Inf 3.0264 1.8773 -1.6690 -2.4673 -2.9800 -3.1631 -3.1736
Inf 3.4963 2.8009 1.6201 -1.6897 -2.4291 -2.7663 -2.8490
Inf 3.5195 2.9999 2.4225 1.5089 -1.7010 -2.3275 -2.4547
Inf 4.2696 3.8015 3.0477 2.3320 1.3838 -1.6491 -1.9703
Inf 4.6241 4.2097 3.6472 2.7803 2.1199 1.5556 -1.1399
Inf Inf Inf Inf Inf Inf Inf Inf
Input Arguments
trans
— Transition probabilities in percent
matrix
Transition probabilities in percent, specified as a
M
-by-N
matrix. 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<N
This implies that thresh
(i,1)
= Inf
, for all i. For example,
suppose that there are only N
=3 ratings,
'High'
, 'Low'
, and
'Default'
, with the following transition
probabilities:
High Low Default High 98.13 1.78 0.09 Low 0.81 95.21 3.98
High Low Default High Inf -2.0814 -3.1214 Low Inf 2.4044 -1.7530
This means the probability of default for 'High'
is
equivalent to drawing a standard normal random number smaller than
−3.1214, or 0.09%. The probability that a 'High'
ends
up the period with a rating of 'Low'
or lower is
equivalent to drawing a standard normal random number smaller than
−2.0814, or 1.87%. From here, the probability of ending with a
'Low'
rating
is:
P[z<-2.0814] - P[z<-3.1214] = 1.87% - 0.09% = 1.78%
'High'
rating
is:100%-1.87% = 98.13%
P[z<Inf
]
Data Types: double
Output Arguments
thresh
— Credit quality thresholds
matrix
Credit quality thresholds, returned as a
M
-by-N
matrix.
References
[1] Gupton, G. M., C. C. Finger, and M. Bhatia. “CreditMetrics.” Technical Document, RiskMetrics Group, Inc., 2007.
Version History
Introduced in R2011b
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