Question

Suppose an FI manager wants to find the probability of default on a two-year loan. For the one-year loan, 1 - p₁= 0.03 is the marginal and total or cumulative probability (Cp) of default in year 1. For the second year, suppose that 1 - p₂= 0.05. Calculate the cumulative probability of default over the next two years.

Answer 1

As per the information shared in the above question:-

Probability of the bond default in the first year = 0.03 or 3%

Hence, the probability that the bond does not default in the first year = (1-0.03) = 0.97 or 97%

Similarly, the Probability of the bond default in the second year = 0.05 or 5%.

Hence, the probability that the bond does not default in the second year = (1-0.05) = 0.95 or 95%

Cumulative probability is a measure that two or more events will happen together. In order to calculate the cumulative probability, we need to multiply the respective probabilities together.

Hence, the cumulative probability that the bond does not default = (0.97*0.95) = 0.9215 or 92.15%

Hence, the cumulative probability of the default over the next 2 years = (1-0.9215) = 0.0785 or 7.85%