Answer: 0.1

## 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)**

Author: LeetQuiz .