The default correlation $\rho$ between two credits can be calculated using the formula:

$\rho = \frac{\pi_{12} - \pi_1 \pi_2}{\sqrt{\pi_1(1-\pi_1)\pi_2(1-\pi_2)}}$

Where:

• $\pi_1 = 0.003$ (default probability of the first credit)
• $\pi_2 = 0.005$ (default probability of the second credit)
• $\pi_{12} = 0.0002$ (joint default probability)

Step 1: Calculate the numerator $\text{Numerator} = 0.0002 - (0.003 \times 0.005) = 0.0002 - 0.000015 = 0.000185$

Step 2: Calculate the denominator $\text{Denominator} = \sqrt{0.003 \times (1 - 0.003) \times 0.005 \times (1 - 0.005)}$ $\text{Denominator} = \sqrt{0.003 \times 0.997 \times 0.005 \times 0.995}$ $\text{Denominator} = \sqrt{0.002991 \times 0.004975} = \sqrt{0.000014880225} \approx 0.0038575$

Step 3: Calculate the correlation $\rho = \frac{0.000185}{0.0038575} \approx 0.047958$

This rounds to $0.04796$. Note that both option a) and option d) are identical and contain the correct value.