Explanation

To calculate the implied default correlation, we use the formula for the correlation between two default events:

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

Where:

• P(A) = 0.02 (2% default probability for BB-rated credit)
• P(B) = 0.03 (3% default probability for BB-rated credit)
• P(A ∩ B) = 0.004 (0.4% joint default probability)

Substituting the values:

$\rho = \frac{0.004 - (0.02)(0.03)}{\sqrt{(0.02)(0.98)(0.03)(0.97)}}$

$\rho = \frac{0.004 - 0.0006}{\sqrt{(0.0196)(0.0291)}}$

$\rho = \frac{0.0034}{\sqrt{0.00057036}}$

$\rho = \frac{0.0034}{0.02388} = 0.1424$

Wait, this gives us 0.1424, which corresponds to option C. Let me recalculate carefully:

Numerator: 0.004 - (0.02 × 0.03) = 0.004 - 0.0006 = 0.0034

Denominator: √[(0.02 × 0.98) × (0.03 × 0.97)] = √[(0.0196) × (0.0291)] = √[0.00057036] = 0.02388

Correlation = 0.0034 / 0.02388 = 0.1424

This matches option C. However, the question asks for the "nearest" answer, and 0.1424 is exactly option C. Let me verify if there might be a calculation error in the original question or if rounding is involved.

Actually, let me recalculate with more precision:

• P(A) = 0.02
• P(B) = 0.03
• P(A∩B) = 0.004
• P(A)P(B) = 0.02 × 0.03 = 0.0006
• P(A)(1-P(A)) = 0.02 × 0.98 = 0.0196
• P(B)(1-P(B)) = 0.03 × 0.97 = 0.0291
• Denominator = √(0.0196 × 0.0291) = √(0.00057036) = 0.023883
• Correlation = (0.004 - 0.0006) / 0.023883 = 0.0034 / 0.023883 = 0.1424

The calculation confirms that the implied default correlation is exactly 0.1424, which corresponds to option C.