Explanation

To solve this problem, we need to understand the relationship between default correlation and joint default probability in a single-factor credit model.

Given:

• Default correlation = 4.9% = 0.049
• Individual default probability (PD) = 2% = 0.02 for both credits
• Joint default probability follows bivariate standard normal distribution

Key Formula: The joint default probability (JDP) can be calculated using: $JDP = \Phi_2(\Phi^{-1}(PD), \Phi^{-1}(PD); \rho)$ where:

• $\Phi_2$ is the bivariate standard normal CDF
• $\Phi^{-1}$ is the inverse standard normal CDF
• $\rho$ is the asset correlation

Calculating the theoretical joint default probability: Given default correlation = 0.049 and PD = 0.02, we can calculate the theoretical JDP: $JDP_{theoretical} = PD^2 + \rho_{default} \times PD \times (1-PD)$ $JDP_{theoretical} = (0.02)^2 + 0.049 \times 0.02 \times (1-0.02)$ $JDP_{theoretical} = 0.0004 + 0.049 \times 0.02 \times 0.98$ $JDP_{theoretical} = 0.0004 + 0.0009604$ $JDP_{theoretical} = 0.0013604 = 0.13604\%$

Matching with the table: Looking at the table, we need to find which asset correlation gives a joint default probability closest to 0.13604%:

• Asset correlation 0.25 → JDP = 0.136%
• Asset correlation 0.20 → JDP = 0.110%
• Asset correlation 0.15 → JDP = 0.040%
• Asset correlation 0.10 → JDP = 0.069%

Conclusion: The asset correlation of 0.25 gives a joint default probability of 0.136%, which matches our calculated theoretical JDP of 0.13604% most closely. Therefore, the implied asset correlation is 0.25.

Answer: D (0.25)