Explanation:
To calculate the probability that a loan currently rated B will default over a two-year period, we need to consider all possible paths that could lead to default (rating D) within two years.
Step 1: Identify possible paths to default in 2 years
From the transition matrix:
Step 2: Calculate total probability
Total probability = Direct default in year 1 + Default via C in year 2 + Default via B in year 2 = 0.10 + 0.06 + 0.075 = 0.235 = 23.5%
Step 3: Verify calculation
The calculation considers all possible transitions:
Total = 0.10 + 0.06 + 0.075 = 0.235 = 23.5%
Therefore, the correct answer is 23.5%.
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As a result of the credit crunch, a small retail bank wants to better predict and model the likelihood that its larger commercial loans might default. It is developing an internal ratings-based approach to assess its commercial customers. Given this one-year transition matrix, what is the probability that a loan currently rated at B will default over a two-year period?
| Rating at Beginning of Period | Rating at End of Period | |||
|---|---|---|---|---|
| A | B | C | D | |
| A | 0.90 | 0.10 | 0.00 | 0.00 |
| B | 0.00 | 0.75 | 0.15 | 0.10 |
| C | 0.00 | 0.05 | 0.55 | 0.40 |
A
17.50%
B
20.0%
C
21.1%
D
23.5%