It depends on what you want to do.
First of all, read this article - it's not the same question, but it talks about the same problem that you'll face here. Namely, that when a default event occurs, it is not always isolated.
(assume that the EURUSD fwd curve F(t) = 1.0 - i.e. the forward curve is just a flat 1 everywhere)
Think about the following four trades:
Google default, you get \$1mm
Google defaults, you get €1mm
Your local family run Pizza co. defaults, you get \$1mm
Your local family run Pizza co. defaults, you get €1mm
We now have a few things to think about:
- What you would expect to happen to the EURUSD exchange rate if
Your local family run Pizza co. defaults - probably nothing - so trades 3 and 4 would be worth the same.
- And the same question if
Google were to default?
- What would you expect to happen if the US economy, as a whole, got into a really bad state?
- What would you expect to happen if the EU economy, as a whole, goes down the toilet?
And the answers:
- I would expect the US economy not to notice the default of a small pizza chain, and so EURUSD is unlikely to change.
- A huge company like
Google defaulting is an entirely different matter - of course it's unlikely to have happened over night, but that doesn't matter - we would expect that EURUSD is going to go up, such that recieving €1mm will now be worth more to you than receiving \$1mm.
- If the US economy tanks, then EURUSD will likely go up, making EURUSD go up, increasing the value of the EUR denominated CDS - but also changing the default probabilities too - small businesses will have a harder time remaining surviving turbulent times than large companies able to weather the storm.
- If the EU gets into a huge mess, then EURUSD will go down, but the default probabilities will remain reasonably unchanged, and the USD denominated CDS instruments will be worth more.
So again, there are now multiple takeaways from this:
If you are speculating, then you will want to chose the denomination which matches your sentiment on the economies, and you'll want to make sure that the difference in price you get for the two matches your perception of the correlation/dependence between the default events and the FX shocks. This will be difficult for you to do anything other than speculate on, as these are going to be sold to you by entities that likely have more information than you do...
If on the other hand (as the title suggests) you are hedging, then you want to use the product which most closely matches the structure you're hedging. If you do not, then you are adding in extra exposure to the "Quanto CDS", which as the FT Alphaville article suggests, is not a trivial product.
As an aside, in your question, you say that you feel there should be a difference in CDS spreads coming from the different shapes of the FX fwd curves. Yes, this is of course true - but there are multiple effects:
- FX forward curves change the weighting of the default probabilities (i.e. the hazard curve) throughout the CDS swap.
- Supply and demand - if there are many trades on XYZ in USD which require the credit risk hedging away, and far fewer in EUR, then this will affect the spreads.
- Correlation/dependence between the default events and FX shocks meaning that the payout, conditional on the default event, are not worth the same, and so must be adjusted.