Credit Risk Management Practice Exam

How is conditional default probability calculated given a constant hazard rate?

1. As λ*t²

2. As λ*e^−λt

3. As λτ

4. As 1 − λτ

The correct answer is: As λτ

The calculation of conditional default probability under a constant hazard rate is a crucial concept in credit risk management. A constant hazard rate (λ) implies a constant likelihood of default per unit time, which is often modeled using an exponential distribution. In this context, the probability of default occurring in a very small interval of time τ can be approximated as λτ. This reflects the fundamental relationship between the hazard rate and the probability of an event (in this case, default) happening in a specified frame of time. When you multiply the constant hazard rate (λ) by the time interval (τ), you are essentially determining the likelihood of default occurring during that short period. This approach is consistent with the properties of survival functions and cumulative distribution functions, where the exponential nature of default risk is captured. While the other options involve mathematical expressions that do not accurately represent the calculation of conditional default probability given a constant hazard rate, option C captures the essence of how to relate the hazard rate to the probability of default effectively.