Serving the Quantitative Finance Community

 
User avatar
quidni
Topic Author
Posts: 11
Joined: November 5th, 2008, 7:32 pm

To "convert" in EUR a USD Sovereing curve (?)

February 15th, 2022, 4:26 pm

Hi all,

excuse me, I have a doubt. If I want to price a fixed rate plain vanilla bond, denominated in USD, and for this want to discount its cashflows by using a USD Sovereign Curve, and then to convert this price into EUR, for example, I first discount its cashflows by using the USD curve, and then convert the final (USD) price into the EUR one by applying the spot USD/EUR rate. Ok.

But, it could make sense to convert the USD Sovereing Curve, into a EUR curve? So that I may get the final price in EUR directly using this curve (to discount its cashflows)? I don't think it makes sense to apply the spot or even forward USD/EUR rate to the USD curve, but do you know or suggest some methodology?

Thanks
 
User avatar
bearish
Posts: 5188
Joined: February 3rd, 2011, 2:19 pm

Re: To "convert" in EUR a USD Sovereing curve (?)

February 15th, 2022, 4:38 pm

At least conceptually you can translate each future USD cash flow into its EUR equivalent by multiplying it by the current forward exchange rate for its payment date. You can then discount this back to the present with your EUR discount factor. What makes the two approaches equivalent is that the (theoretical) forward exchange rate is given by the spot exchange rate times the ratio of the USD to the EUR discount factors.
 
User avatar
quidni
Topic Author
Posts: 11
Joined: November 5th, 2008, 7:32 pm

Re: To "convert" in EUR a USD Sovereing curve (?)

February 15th, 2022, 5:05 pm

Ok thanks! But this is different from instead trying to convert the USD Sovereing curve into a EUR one, right? And this instead properly could make sense, or not?
 
User avatar
bearish
Posts: 5188
Joined: February 3rd, 2011, 2:19 pm

Re: To "convert" in EUR a USD Sovereing curve (?)

February 15th, 2022, 8:00 pm

I don’t know. You seem to be trying to convert a trivial problem into a hard one. And it’s sovereign.
 
User avatar
DavidJN
Posts: 242
Joined: July 14th, 2002, 3:00 am

Re: To "convert" in EUR a USD Sovereing curve (?)

February 15th, 2022, 10:39 pm

What do you mean by “trying to convert the USD Sovereign curve into a EUR one”? Both are already readily observable.
 
There are four interrelated things here: spot FX, the two country yield curves and the term structure of fx forward rates. Give any three of these you can derive the fourth. Is that what you are asking about? Can you reconstruct the EUR yield curve given the other three? Yes, if the counterparties have zero credit risk. The existence of issuer risk premiums, even sovereign risk premiums, can confound the no-arbitrage logic that defines the relationship between these four things, or at least make them considerably more complicated.
 
User avatar
quidni
Topic Author
Posts: 11
Joined: November 5th, 2008, 7:32 pm

Re: To "convert" in EUR a USD Sovereing curve (?)

February 16th, 2022, 3:25 pm

Ah... but so, DavidJN, if I have the FX spot and forward rates, and the USD yield curve, I can derive the correspondant EUR yield curve? In which way?
 
nemozen
Posts: 1
Joined: March 25th, 2022, 4:48 am

Re: To "convert" in EUR a USD Sovereing curve (?)

April 10th, 2022, 10:42 am

There is something called Cross Currency Swap is designed to do this specifically, maybe you want to search a bit on it.