Description Usage Arguments Details Value Author(s) References See Also Examples
cm.cs
computes the credit spreads for each rating of a one year empirical
migration matrix. The failure limit is the quantile of the failure probability.
1 | cm.cs(M, lgd)
|
M |
one year empirical migration matrix, where the last row gives the default class. |
lgd |
loss given default |
This function computes the credit spreads for each rating of a given one year empirical migration matrix with a default class in the last row. The credit spread is the risk premium demanded by the market.
According migration the nominal is differently calculated
V_0 = V_t e^{-(r_t + CS_t) t}
where t is the time. Under a riskless probability measure the value of a credit position at time t is computed as
V_0 = E[V_t] e^{-r_t t}
The default event is bernoulli distributed, so the expected value is
E[V_t] = V_t (1 - PD_t) + V_t (1 - LGD) PD_t
By using the above equations and following transformation, we get the formula for the credit spread
CS_t = - (\ln(1 - LGD PD_t)) / t
This function computes the credit spread for t = 1, this is the credit spread for one year is calculated.
Return value is the credit spread for time t = 1 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 14 15 | lgd <- 0.45
# 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.cs(M, lgd)
|
AAA AA A BBB BB B
4.500101e-05 4.500101e-05 2.700365e-04 8.103282e-04 4.781413e-03 2.367813e-02
CCC
9.327276e-02
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