How to apply PD term structure?

Question

I have a table containing PD term structure with their varying PD values over time such as below:

Now, if I know the starting value of a PD (for e.g. 0.0025), how can i canculate its value in a given year, let's say in year 4 using the above table. Any help?

Answer 1

By the looks of it your table is cumulative PD.

You can use the argument:

$$P(\text{Default by end year X}) = P(\text{Def. by end year X-1}) + P(\text{Not def. by end year X-1})P(\text{Def. in year X}) $$

So that,

$$ P(\text{Def. in year X}) = \frac{P(\text{Def. by end year X})-P(\text{Def. by end year X-1}) }{1-P(\text{Def. by end year X-1})} $$