Explanation

Correct Answer: B

This question involves calculating unconditional default probabilities using hazard rate models. The key concepts are:

Mathematical Framework:

• Hazard rate (λ): Instantaneous default probability
• Survival probability: $S(t) = e^{-λt}$
• Cumulative default probability: $PD(t) = 1 - e^{-λt}$

Calculation Breakdown:

• The unconditional default probability between years 1-2 is given as 0.9656%
• This represents the probability of default occurring specifically in the second year
• The survival rate during the first year is calculated as: $e^{-λ_1 \times 1} = e^{-2\% \times 2} + 0.9656\% = 0.9704$

Interpretation:

• The borrower has a 97.04% probability of surviving the first year
• The 0.9656% represents the marginal default probability in year 2, conditional on survival through year 1