
Explanation:
Defaults shown are cumulative. As such,
P(survival to end of year 2) = 100% − cumulative default rate up to the end of year 2
= 100 − 3.083 = 96.917%
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Q.3052 John is the chief risk officer at a large European bank. While giving a presentation at a quarterly board meeting he got stuck in calculating the probability relevant to the ‘Ba’ rated bond surviving until the end of year 2. Using the below table what is the probability that the ‘Ba’ rated bond will survive until the end of year 2?
Average cumulative default rates (%),1970-2012, from Moody's.
| Term (years): | 1 | 2 | 3 | 4 | 5 | 7 | 10 | 15 | 20 |
|---|---|---|---|---|---|---|---|---|---|
| Aaa | 0.000 | 0.013 | 0.013 | 0.037 | 0.106 | 0.247 | 0.503 | 0.935 | 1.104 |
| Aa | 0.022 | 0.069 | 0.139 | 0.256 | 0.383 | 0.621 | 0.922 | 1.756 | 3.135 |
| A | 0.063 | 0.203 | 0.414 | 0.625 | 0.870 | 1.441 | 2.480 | 4.255 | 6.841 |
| Baa | 0.177 | 0.495 | 0.894 | 1.369 | 1.877 | 2.927 | 4.740 | 8.628 | 12.483 |
| Ba | 1.112 | 3.083 | 5.424 | 7.934 | 10.189 | 14.117 | 19.708 | 29.172 | 36.321 |
| B | 4.051 | 9.608 | 15.216 | 20.134 | 24.613 | 32.747 | 41.947 | 52.217 | 58.084 |
| Caa – C | 16.448 | 27.867 | 36.908 | 44.128 | 50.366 | 58.302 | 69.483 | 79.178 | 81.248 |
A
94.576%
B
98.888%
C
96.917%
D
95.805%
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