Sorry, this might be basic for some of you but I'm very confused when it comes to know which curve (6m or 3m) we can use for valuations of swaps and swaptions. Could someone please explain when to use the 6M curve or 3M curve ? and why ? Thank you
You use the curve that describes the floating rate index to estimate the floating rate cashflows, a swap against floating 3M uses a 3M curve to forecast the cashflows.
And then you use a discounting curve to discount the future cashflows that aligns with the funding/collateralisation of the derivative. For example almost all cleared swaps will use the OIS curve for discounting. Very few use either the 3M or 6M curve.