The method to connect interest rate swap conditions is to employ forward-implied rates. The forward price of a currency must relate to an interest-rate differential between two currencies. The classic definition says it assumes an arbitrage condition is possible if parity doesn't exist.
A formula to look at this relationship is:
ti* = foreign period nominal interest rate,
it = domestic period interest rate,
st = spot rate (foreign to domestic in logs),
set+1 = market one step ahead forecast for the spot rate at t, and
pt = risk premium.
This formula captures bond-yield differentials that reflect expected exchange-rate ...