Answer: 23.1%

The implied default correlation for the credit portfolio is calculated using the formula for default correlation (p12), which is derived from the individual probabilities of default (π1 and π2) and the joint probability of default (π12). The formula is as follows: \[ P_{12} = \frac{π_{12} - π_1 \times π_2}{(1 - π_1) \times (1 - π_2)} \] Given the probabilities of default for the BBB-rated credit (π1) as 3.5% and the BB-rated credit (π2) as 4.2%, and the joint default probability (π12) as 1.0%, we can plug these values into the formula: \[ P_{12} = \frac{1.0\% - 3.5\% \times 4.2\%}{(1 - 3.5\%) \times (1 - 4.2\%)} \] \[ P_{12} = \frac{1\% - 0.147\%}{0.965 \times 0.958} \] \[ P_{12} = \frac{0.853\%}{0.92418} \] \[ P_{12} \approx 0.23139 \text{ or } 23.14\% \] Thus, the implied default correlation for the credit portfolio for the next year is approximately 23.14%, which corresponds to option C. This calculation is important in credit risk management as it helps in understanding the relationship and dependency between the defaults of different credits within a portfolio, which is crucial for assessing and managing the overall credit risk.

Author: LeetQuiz Editorial Team