The correct answer is C, which represents a risk-neutral probability of 21.34% that the bond rated BBB defaults within the next 3 years. This is calculated using the continuously compounded 3-year spread for the bond, which is 8% per year (0.10 - 0.02). Given the expected recovery rate of 0% in the event of default, the hazard rate is equal to the spread, which is also 8% per year. The formula to calculate the risk-neutral probability of default over time $t$ is $1 - \exp(-\text{hazard rate} \times t)$. Substituting the values, we get $1 - \exp(-0.08 \times 3) = 21.34\%$. The other options are incorrect for the following reasons:

• Option A (6.55%) is the marginal probability of default in the third year for the 3-year BBB-rated bond, not the cumulative probability over 3 years.
• Option B (14.55%) incorrectly uses the credit spreads of the 1-year, 2-year, and 3-year bonds rated BBB and does not properly scale the hazard rates by the factor of time.
• Option D (25.92%) incorrectly assumes the hazard rate for the 3-year bond rated BBB is equal to its annual yield of 10%, rather than using the spread adjusted for the risk-free rate.