transprobfromthresholds
Convert from credit quality thresholds to transition probabilities
Description
Examples
Transform Credit Quality Thresholds Into Transition Probabilities
Use historical credit rating input data from Data_TransProb.mat
, estimate transition probabilities with default settings.
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
Recover the transition probabilities.
trans = transprobfromthresholds(thresh)
trans = 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
Input Arguments
thresh
— Credit quality thresholds
matrix
Credit quality thresholds, specified as a
M
-by-N
matrix of credit
quality thresholds.
In each row, the first element must be Inf
and the
entries must satisfy the following monotonicity
condition:
thresh(i,j) >= thresh(i,j+1), for 1<=j<N
The M
-by-N
input
thresh
and the
M
-by-N
output
trans
are related as follows. The 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
Any given row in the output matrix trans
determines a probability distribution over a discrete set of
N
ratings 'R1'
,
...
, 'RN'
, so that for any row
i
trans
(i,j) is
the probability of migrating into
'Rj'
.
trans
can be a standard transition matrix, with
M
≤ N
, in which case 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
.
For example, suppose that there are only N
=3
ratings, 'High'
, 'Low'
, and
'Default'
, with these credit quality
thresholds:
High Low Default High Inf -2.0814 -3.1214 Low Inf 2.4044 -1.7530
High Low Default High 98.13 1.78 0.09 Low 0.81 95.21 3.98
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
trans
— Matrix of transition probabilities in percent
matrix
Matrix of transition probabilities in percent, 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
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)