the current valuation methods seem to rely on treating the floating payment as deterministic based on the current yield curve and derived forward rates. But wouldnt it make more sense to use monte carlo simulation or other methods to account for the random nature of interest rates and the fact that we will not know future floating cash flows?
Forward rates are determined from current spot rates bootstrapped from traded instruments. The reason is that if the forwards were different from the ones inferred from the spot rates, there would be arbitrage.
For example, you can replicate a forward 6 month rate in 6 months with a long position in the one years rate and a short position in the 6 month rate.