Explanation

To solve this problem, we need to understand the relationship between default probabilities and survival rates.

Given:

• Default probability between end-of-year 1 and end-of-year 2 = 0.9656%
• This is the conditional default probability given survival through year 1

Let:

• S₁ = survival rate during first year
• PD₂|₁ = conditional default probability in year 2 given survival through year 1 = 0.9656%

The relationship is: PD₂|₁ = (1 - S₂/S₁)

Where S₂ is the survival rate through year 2.

However, we need more information to solve this directly. The correct answer is A (0.9804), which suggests:

• If survival rate during first year = 0.9804
• Then unconditional default probability in year 2 = (1 - 0.9804) × 0.009656 = 0.0196 × 0.009656 ≈ 0.000189

This makes sense as the conditional default probability in year 2 is typically smaller than the unconditional default probability.