What's the time horizon of the probability of default implied from a CDS spread? Given CDS = PD*(1-R), if I use a 5yr CDS spread in the formula, is the implied PD the probability that that name defaults within the next 5 years or 1 year given it represents the annual premium?
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1$\begingroup$ The statement $CDS\approx PD(1-R)$ is only a very rough estimate. An $N$-year CDS conveys market-implied / risk-neutral default probabilities for a default at any date up until the maturity date of the CDS. You can use a series of increasing maturities to back out risk-neutral conditional default probabilities, i.e. implied probabilities of default during a year $N$. $\endgroup$– KermittfrogNov 25, 2020 at 15:12
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CDS quotes are observable. But none of: probabilities of default, hazard rates, loss given default/recovery, etc are observable.
To get some kind of (risk-neutral) probabilities of default, many people make a lot of assumptions, in particular, that the hazard rate is constant (or if you're lucky enough to have CDS quotes at more than one tenor, then piecewise constant between quotes). Then they solve numerically for the hazard rates that explain the obsevable quotes and assumptions. Interest rates play a minor role. Some people use more sophisticated assumptions, such as term structure of recovery, or fancier curve shapes.
Once you have the hazard rates, it's easy to read off both the probability that there will be a default within $n$ years and the marginal probability that, provides there has not been a default until $n$, there will be one between $n$ and $m$.
The formula you cite is a very rough approximation of the probability that there will be a default before the maturity if the CDS.
answered Nov 25, 2020 at 16:02
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$\begingroup$ Just to clarify, if I have as data only the spread of a 5yr CDS, would it be a better approximation to calculate the probability of default within the next 5 years with which of these two methods? 1) Derive 1yr PD from CDS = PD*(1-R) and then multiply this by 5 (mentioned above) or 2) Derive 1yr PD from CDS = PD*(1-R) and then using compounding of survival probability based on P(A and B) = P(A)P(B|A) = 1- (1-PD)^5 $\endgroup$– StudentNov 26, 2020 at 11:22
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$\begingroup$ I don't llike either calculation. :) How about you assume some R, and walk through the SDA CDS Standard Model? $\endgroup$ Nov 26, 2020 at 14:25