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I was asked this question the other day, but it's been years since I've done this work.

If the probability of a company to default in a year is $8\%$, what is the probability that it will default in year 2?

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  • $\begingroup$ Do you have an idea ? or a formula?. Please share it. $\endgroup$ – user16651 Jul 16 '16 at 8:11
  • $\begingroup$ Is this the only information you have? Are you allowed to use default curves of other companies too? Ie sector curves? $\endgroup$ – will Jul 16 '16 at 9:34
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Generally, survival probability can be interpolated or extrapolated log-linearly, which is, at the least, consistent with the piece-wise constant hazard rate assumption. Specifically, let $x$ be the survival probability at year 2. The year 1 survival probability, 92%, can be log-linearly interpolated from the survival probability 1 at year 0 and the survival probability $x$ at year 2, that is, \begin{align*} \ln (0.92) = \ln (1) + \frac{\ln x - \ln (1)}{2-0}\times(1-0). \end{align*} Then \begin{align*} x = 0.92^2 = 84.64\%. \end{align*} Consequently, the default probability at year 2 is $15.36\%$.

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I guess with that very sparse information all you could do is take the probability that the company still exists in a year (92%) times 8 % (assuming that the probability itself does not change). I believe I had something similar in an exam once. However, it is a really simplistic answer.

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