If the marginal probabilities of default for a corporate bond for years 1, 2 and 3 are 2%, 3% and 4% respectively, what is the cumulative probability of default at the end of year 3?

If the marginal probabilities of default for a corporate bond for years 1, 2 and 3 are 2%, 3% and 4% respectively, what is the cumulative probability of default at the end of year 3?
A . 8.74%
B . 9.58%
C . 9.00%
D . 91.26%

View Answer

Answer: A

Explanation:

Marginal probabilities of default are the probabilities for default for a given period, conditional on survival till the end of the previous period. Cumulative probabilities of default are probabilities of default by a point in time, regardless of when the default occurs. If the marginal probabilities of default for periods 1, 2… n are p1, p2…pn, then cumulative probability of default can be calculated as Cn = 1 – (1 – p1)(1-p2)…(1-pn). For this question, we can calculate the probability of default for year 3 as =1 – (1-2%)*(1-3%)*(1-4%) = 8.74%