What if I want to build a curve to price swaps on Libor 1w, Libor 2m or Libor 2y. According to multiple curve framework, I'd better build those curves by having 1w/3m basis swap, 2m/3m basis swap and 2y/3m basis swap. But as we know, those contracts are not traded at all. In this sense, how should I construct my libor 1w, for example, curve? Should I directly derived from Libor 3m curve by using no arbitrage discounting? What about deriving from OIS curve which has closer credit risk?
Any thoughts from anyone?