As an US investor, if I enter a basis swap in a foreign currency (say Euribor-Eonia basis in EUR), and book my trade using USD. I must have some sort of FX risk, right?
How do I hedge such risk? I'd imagine my delta to EURUSD is 0 at the time I enter this swap. But as market moves, my P&L either positive or negative. Does that mean I need to dynamically hedge this FX risk?
(please feel free to edit if my question isn't phrased clearly)