cm.quantile: Computation of migration quantils

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

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.

Usage

1

Arguments

M

one year empirical migration matrix, where the last row gives the default class.

Details

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.

Value

Return value is the quantile of each rating in the migration matrix.

Author(s)

Andreas Wittmann andreas\_wittmann@gmx.de

References

Glasserman, Paul, Monte Carlo Methods in Financial Engineering, Springer 2004

See Also

cm.matrix, qnorm

Examples

 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)

Example output

                  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

CreditMetrics documentation built on May 2, 2019, 8:55 a.m.