A stock has a probability of jumping to default based on the first arrival of a Poisson process with $\lambda = 0.05$ . What is the probability of a jump-to-default in any month?
A) 0.4158%
B) 0.4167%
C) 0.4195%
D) 0.5000%

Question

Quizplus · Accepted Answer

The probability of a jump-to-default in any month is given by the Poisson distribution with $\lambda = 0.05$. The probability of a jump-to-default in any month is given by:$$P(X = k) = \frac{e^{-\lambda} \lambda^k}{k!}$$where $k$ is the number of jumps-to-default in a month.For $k = 1$, we have:$$P(X = 1) = \frac{e^{-0.05} 0.05^1}{1!} = 0.004158$$Therefore, the probability of a jump-to-default in any month is 0.4158%.

A Stock Has a Probability of Jumping to Default Based λ=0.05\lambda = 0.05λ=0.05

A Stock Has a Probability of Jumping to Default Based $\lambda = 0.05$