To calculate the implied default correlation $\rho$, we use the formula:

$\rho = \frac{P(A \cap B) - P(A)P(B)}{\sqrt{P(A)(1-P(A))P(B)(1-P(B))}}$

Given:

• $P(A) = 0.02$
• $P(B) = 0.03$
• $P(A \cap B) = 0.004$

Substitute the values:

• Numerator $= 0.004 - (0.02 \times 0.03) = 0.004 - 0.0006 = 0.0034$
• Denominator $= \sqrt{0.02 \times 0.98 \times 0.03 \times 0.97} = \sqrt{0.0196 \times 0.0291} = \sqrt{0.00057036} \approx 0.0238822$

$\rho = \frac{0.0034}{0.0238822} \approx 0.142365$

Therefore, the implied default correlation is approximately 0.1424.