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Answer: The unconditional default probability between end-of-year 1 and end-of-year 2 is 0.9656%
## 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
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The unconditional default probability between end-of-year 1 and end-of-year 2 is calculated as follows: . We can thus solve the survival rate of the borrower during the first year of the loan, which is :
A
Option A not provided in the text
B
The unconditional default probability between end-of-year 1 and end-of-year 2 is 0.9656%
C
Option C not provided in the text
D
Option D not provided in the text
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