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?

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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 any 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 $\lambda = 0.05$