Int. Risk sharing in small open economy models

Hello everyone,

I have a tiny question concerning the modelling of international asset markets in open dsge models, as for example in Gali & Monacelli 2005. Actually i do have an idea on the way it works, but i would greatly appreciate if someone could confirm if i am on the right track, even though its not directly dynare-related (sorry about this)!

I am wondering about the intuition behind the working of the well known risk-sharing condition, which emerges from the assumption of an complete set of state-contingent tradable claims.

What i am not sure about is the connection between the risk-sharing condition and the domestic euler equation in small open economy models. Since changes in the domestic real interest rate affects our consumtion, it does also have to affect our real exchange rate (since the risk sharing condition connects changes in relative consumtion to changes in the real exchange rate).
Am i right by the idea that only the uncovered interest parity is responsible for that trick? From the UIP, any movement in our nominal interest rate would affect the nominal exchange rate in a way to align the movements in domestic consumption from the euler equation and the risk-sharing condition.

I hope this question does not bore everyone, but a short confirmation would help me a lot!

many many thanks,