I have to find the CDS's default probability using the simplest Poisson Process (intensity constant).
I'm wondering how to get this estimate if I have only a CDS with maturity 5years.
If I had different maturities I could assume, for example, that the PD (probability of default) related to 1 years is that extracted from the CDS 1 y, then the one related to 2 years is extracted from the CDS with 2-years maturity assuming a pd for the first year equal to the one evaluated before(1year PD) and so on.
So, my question is:
if I have just 1 CDS, as, for instance, the case of iTraxx crossover index, can I compute the PD assuming that this probability remains constant throughout the 5 years?
Do alternative solutions exist?