TheBridge
• 4.4k
• 2
• 28
• 40

I have a little more informations, so let me share it with you.

Even though I think that the frameworks I presented in my question are both corrects (i.e. aribtrage free), it happens to be the case that the market seems to have more "structure".

Here is a methodology that allows to retreive market quotes and which is the same as BBG (which is the best reference I could get in terms of market practice), so for a USD based investor :

Use step 1 and 2 to build multicurve US discount curve (based on Fed Funds) and forward curve for (LibUSD3M)

Use again step 1 and 2 to build multicurve EUR discount curve (based on OIS) and forward curve for Euribor3M.

Then forget about EUR discount curve and build a new discounting EUR curve in the following way, use :
-Cross Currency ATM Swap
-EUR forward Curve
-USD Discount
-USD forward curve
-Spot FX rate

So that you can build a new EUR Discount curve that allows you to retrieve Cross Currency Swaps ATM Quotes.

I have made a few tests to compare my USD based framework and this one and the results are quite similar.

What this really says IMO, is that in whatever economy you are based you have $$E^{FF_T}[Euribor3m(T-3m,T)]$$ and $$E^{OIS_T}[Euribor3m(T-3m,T)]$$ that are almost equals for any $$T$$, where $$E^{FF_T}$$ is the USD-FF T-forward pricing measure and $$E^{OIS_T}$$ is the EUR-OIS T-forward pricing measure (this is what I meant by "the market seems to have more structure" at the beginning of my post).

This was quite surprising to me and if anyone has more insight on this subject I am all ears.

NB : The methodology presented here can be applied for an EUR Based investor aswell with the same conclusions.

Best regards

TheBridge
• 4.4k
• 2
• 28
• 40

I have a little more informations, so let me share it with you.

Even though I think that the frameworks I presented in my question are both corrects (i.e. aribtrage free), it happens to be the case that the market seems to have more "structure".

Here is a methodology that allows to retreive market quotes and which is the same as BBG (which is the best reference I could get in terms of market practice), so for a USD based investor :

Use step 1 and 2 to build multicurve US discount curve (based on Fed Funds) and forward curve for (LibUSD3M)

Use again step 1 and 2 to build multicurve EUR discount curve (based on OIS) and forward curve for Euribor3M.

Then forget about EUR discount curve and build a new discounting EUR curve in the following way, use :
-Cross Currency ATM Swap
-EUR forward Curve
-USD Discount
-USD forward curve
-Spot FX rate

So that you can build a new EUR Discount curve that allows you to retrieve Cross Currency Swaps ATM Quotes.

I have made a few tests to compare my USD based framework and this one and the results are quite similar.

What this really says IMO, is that in whatever economy you are based you have $$E^{FF_T}[Euribor3m(T-3m,T)]$$ and $$E^{OIS_T}[Euribor3m(T-3m,T)]$$ that are almost equals for any $$T$$, where $$E^{FF_T}$$ is the USD-FF T-forward pricing measure and $$E^{OIS_T}$$ is the EUR-OIS T-forward pricing measure.

This was quite surprising to me and if anyone has more insight on this subject I am all ears.

NB : The methodology presented here can be applied for an EUR Based investor aswell with the same conclusions.

Best regards