Explanation:
To find the probability of default over 2 years for a B-rated company, we need to consider defaults in Year 1 and defaults in Year 2.
Probability of default in Year 1 (Transition from B to D): 3.50%
Probability of default in Year 2 involves transitioning to a non-default rating in Year 1, and then defaulting in Year 2:
$1.00% \times 0.00% = 0.00%$$88.00% \times 3.50% = 3.08%$$7.50% \times 14.50% = 1.0875%$Total probability of default in Year 2 = $0.00% + 3.08% + 1.0875% = 4.1675%$
Cumulative probability of default over 2 years = Default in Year 1 + Default in Year 2 = $3.50% + 4.1675% = 7.6675% \approx 7.7%$
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Q.90 A bank has the following internal rating transition matrix:
Annual Rating Transitions (% , Average Annual)
| A | B | C | D | |
|---|---|---|---|---|
| A | 98.50 | 1.00 | 0.50 | – |
| B | 1.00 | 88.00 | 7.50 | 3.50 |
| C | – | 10.00 | 75.50 | 14.50 |
Based on the matrix, what is the probability of default over 2 years of a company with a rating of B?
A
2.5%
B
4.6%
C
6.8%
D
7.7%
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