
Explanation:
Note that the events of default for the bonds are independent and identically distributed Bernoulli random variables, hence, the Binomial distribution can be used to calculate the probability of exactly one bond defaulting.
The probability mass function of a binomial random variable, K is given by:
Where:
n = the number of bonds in the portfolio
p = the probability of default of each individual bond
k = the number of defaults for which you would like to find the probability.
In our case n = 3, p = 0.10, and k = 1.
So that,
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Q.69 A portfolio consists of three bonds and each bond has a 1-year default probability of 10%. The event of default for each of the bonds is independent. What is the probability of exactly one bond defaulting over the next year?
A
0.243
B
0.1215
C
0.027
D
0.757
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