Description Usage Arguments Details Value Author(s) References See Also Examples
cm.quantile
computes the empirical migration quantils for each rating
of a one year empirical migration matrix. The failure limit is the quantile
of the failure probability.
1 | cm.quantile(M)
|
M |
one year empirical migration matrix, where the last row gives the default class. |
This function computes the empirical migration threshold value of a given one year empirical migration matrix with a default class in the last row. So the migration threshold can be computed with the migration probabilities. Migration quantiles have to be computed for each output rating.
The default threshold value S of the standard normal distribution with expectation 0 and standard deviation 1 gives
S = N^{-1}(PD)
where N^{-1} is the inverse function of the standard normal distribution and PD is the probability of default.
Thus an example for an BBB rated company is
S = N^{-1}(PD_{BBB})
So for each rating class thresholds can be computed.
Return value is the quantile of each rating in the migration matrix.
Andreas Wittmann andreas\_wittmann@gmx.de
Glasserman, Paul, Monte Carlo Methods in Financial Engineering, Springer 2004
1 2 3 4 5 6 7 8 9 10 11 12 13 | # one year empirical migration matrix from standard&poors website
rc <- c("AAA", "AA", "A", "BBB", "BB", "B", "CCC", "D")
M <- matrix(c(90.81, 8.33, 0.68, 0.06, 0.08, 0.02, 0.01, 0.01,
0.70, 90.65, 7.79, 0.64, 0.06, 0.13, 0.02, 0.01,
0.09, 2.27, 91.05, 5.52, 0.74, 0.26, 0.01, 0.06,
0.02, 0.33, 5.95, 85.93, 5.30, 1.17, 1.12, 0.18,
0.03, 0.14, 0.67, 7.73, 80.53, 8.84, 1.00, 1.06,
0.01, 0.11, 0.24, 0.43, 6.48, 83.46, 4.07, 5.20,
0.21, 0, 0.22, 1.30, 2.38, 11.24, 64.86, 19.79,
0, 0, 0, 0, 0, 0, 0, 100
)/100, 8, 8, dimnames = list(rc, rc), byrow = TRUE)
cm.quantile(M)
|
D CCC B BB BBB A AA
AAA -Inf -3.7190165 -3.540084 -3.352795 -3.035672 -2.911238 -2.382404 -1.329145
AA -Inf -3.7190165 -3.431614 -2.947843 -2.847963 -2.382404 -1.362627 2.457263
A -Inf -3.2388801 -3.194651 -2.716381 -2.300852 -1.507042 1.984501 3.121389
BBB -Inf -2.9112377 -2.226212 -1.965123 -1.420714 1.530068 2.696844 3.540084
BB -Inf -2.3044036 -2.041512 -1.231864 1.367719 2.391056 2.929050 3.431614
B -Inf -1.6257634 -1.324310 1.455973 2.413503 2.687449 3.035672 3.719016
CCC -Inf -0.8491461 1.021537 1.738061 2.113009 2.627559 2.862736 2.862736
AAA
AAA Inf
AA Inf
A Inf
BBB Inf
BB Inf
B 8.209536
CCC Inf
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