Answer: 23.1%

The implied default correlation for the credit portfolio is calculated using the formula provided in the file content. The formula is designed to find the correlation coefficient (p12) between the default probabilities of two credit assets. The default probabilities given are π1 = 3.5% for the BBB-rated credit and π2 = 4.2% for the BB-rated credit. The joint default probability, π12, is 1.0%. The formula to calculate the implied default correlation is: \[ P_{12} = \frac{\pi_{12}}{\pi_1 \times (1 - \pi_1) \times \pi_2 \times (1 - \pi_2)} \] Plugging in the given values: \[ P_{12} = \frac{1\%}{3.5\% \times (1 - 3.5\%) \times 4.2\% \times (1 - 4.2\%)} \] \[ P_{12} = \frac{1\%}{3.5\% \times 96.5\% \times 4.2\% \times 95.8\%} \] \[ P_{12} = \frac{1\%}{0.0351 \times 0.0414 \times 0.9648} \] \[ P_{12} = 0.23139 \text{ or } 23.14\% \] This calculation shows that the implied default correlation for the credit portfolio is 23.14%, which corresponds to option C. The other options (A, B, and D) are incorrect because they either add the probabilities incorrectly or use a wrong formula operation. The correct answer is derived using the proper formula for default correlation, which accounts for the individual default probabilities and their joint default probability.

Author: LeetQuiz Editorial Team