Credit Risk Management Practice Exam

What mathematical operation is used to compute marginal probability of default from hazard rate?

1. Summation of previous defaults

2. λ*e^−λt

3. Multiplication of survival rates

4. Integration of past data

The correct answer is: λ*e^−λt

To compute the marginal probability of default from the hazard rate, the correct operation involves using the formula λ*e^−λt, which relates the hazard rate (λ) to the probability of default over a specific time period (t). The hazard rate represents the instantaneous rate of default at any given time, and this equation uses the exponential function to account for the survival probability over time. In this context, the term e^−λt represents the probability that a borrower has survived without defaulting up to time t. By multiplying this survival probability by the hazard rate (λ), the formula yields the marginal probability of defaulting at that specific time. Therefore, it is a mathematically expressed relationship that transitions from hazard rates to default probabilities, critical for risk assessments in credit management. The other options do not provide the correct relationship needed for calculating marginal probability of default from the hazard rate.