# Extracting Default probability from a single CDS

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?

• You should not assume that the probability stays constant. But you can assume that the probability is driven by a hazard rate that remains constant. This is standard industry practice. – Dimitri Vulis Aug 20 '19 at 23:25

Yes, you can assume that, since you cannot extract the probability of default for shorter maturity, but for the 5-years only CDS one, because of unavailability of data.

Of course, you'll have to update with shorter frequency your estimate, because the extracted PD will change overtime and the $PD_t$ could be different from $PD_{t+1}$, according to the macroeconomic scenarios will affect the economy.

I suggest you to take a cue from:

Byström, Hans. "Credit default swaps and equity prices: The iTraxx CDS index market." Working Papers, Department of Economics, Lund University 24 (2005).

to understand how one analyze that kind of index and, consequently, construct the scenarios to which the CDS is exposed and how the extracted PD could change overtime.

Hope this helps.

It is not a direct answer to your question, but if the real problem is the lack of data, you can check www.datagrapple.com for spreads on the tenors 1, 3, 5, 7 and 10 years for coporate, financial, sovereign CDS and iTraxx / CDX indices.