That is really extensive question. I am no longer part of CVA desk, but I'll answer on this question, based on my experience.
So, let's take a look at your first question. The CDS is a credit derivative, which price demonstrates a spread (sometimes with a multiplier) between bond/debt/protected asset buyer and seller, and it can be interpreted as a probability of the default. There are index products, like a «pan-American» CDX or «pan-European» iTraxx and a single-names protection.
At this point let's take a look a this website called WorldGovernmentBonds
I am not 100% sure that its data represent the actual market. I don't take any responsibility and so on. Anyway, it's not IHS Markit, BUT, to be honest we don't need to an actual CDS data to answer first question, and this site does represent the perfect example situation.
So as you may see, the CDS price is usually correlated with SP rating, and PD can be evaluated from CDS price & VaR metrics, but it's kinda.. well, we calculating the underlying event probability, based on price of derivative, which price and volatility shows us the % change of underlying (credit) event*.
We should always remember, that
default !== credit event, the responsibility of the protection seller, is a different problem in another field and a very complicated question. Such as amount of Recovery and so on.
You might also saw a relevant question on QuantFinance about it How to compute the implied probability of default from a CDS spread? and you may already found Nomura's PDF with necessary formulas, which is an answer to your question.
- Is the probability of default constant over the time steps?
If we are talking about CDS prices, — no. It depends on tenor and it's volatility. But it's a bit more complicated than that. For example, imagine yourself an
N axis matrix, like:
- SP rating [AAA -> SD]
- Industry [Mining -> HealthCare]
- Operation Region [EMEA -> APAC]
- Any other relevant axis, like T (time)
This awfully long 145 page
*.pdf might help you to understanding it. As I mentioned above, and you may seen it by yourself, in most cases CDS price is correlated with SP rating (and with PD itself). So for each single name (company) PD is always compared to other company in the operating region / industry sector / (relevance criteria) and so on. So it's constant, not over time steps, but over each other.
This 45 page
*.pdf is a bit irrelevant, but you might find it useful in your case. Cause it's demonstrates rating change within different time periods.
Might, you find my answer useful.