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As you know, with basic assumptions default probability could be calculated by

$$\text{CDS Spread} = p \cdot \frac{1-RR}{1+r}$$

Does that make sense to use 5 Year CDS Spread with 5 year Generic Government Bond Yield as risk-free rate?

If yes, most CDSs are written of USD.

Which one is okay to use US Government bond or Country's Government which is bank operates? It seems currency mismatch to me: if I calculate a German bank's default, I would use the CDS spread of the bank (which is $ Denominated) and rate of Germany Bond? Would that make sense?

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Normally for USD denominated CDS you should use US government bonds as the risk free rate. As a general rule debt is more likely to be risk free if it is issued in the government's currency.

If you take a high credit risk country (for instance Venezuela), then using Venezuela government USD yield as the risk free rate you will end up having a wrong probability of default.

PDVSA which is the venezuelian petroleum exporter has a 5Y CDS at 4 898 bp, Venezuela @ 4 004 bp. Your risk free rate isn't exactly risk free and a 900 bp credit spread won't give you the same probability of default than the 4870 bp credit spread that better reflects the actual risk and probability of default.

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  • $\begingroup$ I'm not sure I understand your Venezuela example. Could you clarify? $\endgroup$
    – SRKX
    Dec 29, 2016 at 4:02
  • $\begingroup$ You can not take Sovereign Venezuela USD as a risk free rate, a risk free rate in a given currency is more likely to be from the issuer with the highest control on the currency. I took Venezuela because actually German USD CDS is currently nearly equal to United States USD CDS. Venezuela VEF bonds rate would be the most appropriate if you were to study VEF CDS. $\endgroup$
    – Lliane
    Dec 29, 2016 at 4:27

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