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.