Answer: 0.1393

## Explanation For a hazard rate (default intensity) λ = 0.15, the probability of default in year 2 given survival through year 1 is calculated using the exponential distribution. **Step-by-step calculation:** 1. **Hazard rate interpretation**: The hazard rate λ = 0.15 means the instantaneous default probability is 15% per year. 2. **Probability of default in year 2 given survival through year 1**: - This is equivalent to P(default between t=1 and t=2 | survival to t=1) - For a Poisson process with constant hazard rate λ, this probability is: \[ P(\text{default in year 2} | \text{survival through year 1}) = 1 - e^{-\lambda} = 1 - e^{-0.15} \] 3. **Calculation**: \[ 1 - e^{-0.15} = 1 - e^{-0.15} = 1 - 0.8607 = 0.1393 \] **Verification**: - The survival probability through year 1 is e^{-0.15} = 0.8607 - The probability of default in year 2 given survival through year 1 is indeed 0.1393 Therefore, the correct answer is **A. 0.1393**.

Author: LeetQuiz .