Choosing a Currency-Consistent Risk-Free Rate for CDS Default Estimates

Summary

The document addresses which interest rate to use when translating a credit default swap spread into an approximate default probability. Its answer ties the risk-free benchmark to the currency of the CDS: for a US-dollar-denominated contract, it recommends a US government rate rather than the operating country’s government yield. The rationale is that government debt is more plausibly risk-free when issued in the government’s own currency.

A sovereign with substantial credit risk is a poor risk-free proxy, even if its bonds are denominated in dollars. The example contrasts spreads on a Venezuelan company’s CDS and Venezuela’s own CDS to show how treating the sovereign yield as risk-free could understate the credit spread relevant to default estimation. This is a simplified framework: the stated spread relationship depends on assumptions about recovery and discounting, and the brief answer does not develop a complete CDS valuation or probability model. Currency matching is the central practical lesson.

Key ideas

• Choose a risk-free benchmark consistent with the currency denomination of the CDS.
• For a dollar-denominated CDS, the answer recommends using a US government rate.
• A risky sovereign’s yield is not an appropriate risk-free rate merely because it is available in the contract currency.
• The spread-to-default-probability relationship is presented as a simplified estimate.

Tags

# Which interest rate to choose to estimate a CDS default probability?


# Which interest rate to choose to estimate a CDS default probability?












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?

## Answer by Lliane (score 0, accepted)

https://quant.stackexchange.com/a/31702

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.