Answer: 8.17%

## Explanation To calculate the conditional probability of default during year 3, we need to follow these steps: ### Step 1: Calculate Unconditional PD for Year 3 Unconditional PD in year 3 = Cumulative PD in year 3 - Cumulative PD in year 2 \[ 39.86\% - 34.51\% = 5.35\% \] ### Step 2: Calculate Survival Rate to Year 3 Survival rate to year 3 = 100% - Cumulative PD to year 2 \[ 100\% - 34.51\% = 65.49\% \] ### Step 3: Calculate Conditional PD in Year 3 Conditional PD in year 3 = Unconditional PD in year 3 / Survival rate to year 3 \[ \frac{5.35\%}{65.49\%} = 8.17\% \] ### Why Other Options Are Incorrect: - **A (5.35%)**: This is the unconditional PD in year 3, not the conditional PD - **C (19.90%)**: This incorrectly applies hazard rate formulas - **D (26.10%)**: This incorrectly multiplies survival rate by cumulative PD The conditional probability represents the likelihood of default during year 3 given that the bond has survived up to the beginning of year 3.

Author: LeetQuiz .