Let say I have 2 Forward start Float-Float Interest Rate Swaps starting in 1 year and 2 years and both have 5 years of life.
I know the prices of both these swaps say $P_1$ and $P_2$
Given this information, is it possible to derive the price of Spot starting swap with the same maturity of 5 years?
If not, then what other information is required to derive the price of the spot starting swap? All these 3 swaps have same indices for cash-flows at both legs (e.g. 3m libor vs 6m libor)
Any pointer will be highly appreciated.