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Hi,I am trying to settle a bet and would appreciate your help.For the valuation of a vanilla cross-currency swap, 3M USD vs 3M EURIBOR with final principal exchange, a colleague of mine is arguing that you do not need to use the respective forward curves. His argument is that (and I quote):===================================================================================================the cross currency interest rate swap is a series of FRAs with the forward rate being the spot rate plus the forward premium (the forward premium represents the interest rate differential difference between the currenciesat any point during the life of the forward contract the value of the contract is calculated as the contracted forward rate minus the then prevailing forward rate for the remaining term to maturity multiplied by the notional amount as the contract approaches maturity the forward rate converges on the spot rate such that at maturity the forward rate equals the spot rate (because as there is no remaining term to maturity there is no discount period and the interest rate differential no longer matters). On the maturity date for a single FRA (the reset date for the swap) the interest is paid and the value of the swap is simply the EUR notional minus the USD notional converted at the then prevailing spot rate. Since the interest rate differential has no impact (as explained above) on the reset date the value of the swap is entirely attributable to the difference between the swap rate and the current spot exchange rate. On the swap reset date the Company effectively enters into a new FRA at the then prevailing forward rate (which is the then prevailing spot rate plus/minus the forward premium/ discount). But this could have been anyway using a single FRA so the fact that the swap allows it to do this does not provide any value. Therefore future interest rates/ curves are irrelevant to the swap valuation. =========================================================================================I am pretty sure he's is incorrect in that both the ccy basis and the full value of the final principal exchange are not being accounted for. However, if somebody has a more concise explanation of his error or could point me towards a reference it could be quite lucrative for me.

Why FRAs? Let's assume Libor discounting. Then receiving the floating leg is the same as receiving the principal at the first setting date T_0 and paying the principal at maturity. So floating leg minus principal at maturity is equal to principal at T_0.The value is P(t,T_0).The value of the cross-currency floating swap is then: P(t,T_0)^USD - FX_t.P(t,T_0)^EUR plus the basis swap bewteen 6m and 3m EUR libors. I would say the answer is yes with Libor discounting and no with another discounting?