The concepts of marginal vs incremental are rather general, eg. can relate to VAR, CVA, etc.
Marginal refers to a change in a metric (eg. CVA) due to a (infinite)small change to a position (eg. Adding $1 or 1 share to existing position).
Incremental refers to a conribution of a position as a...
Your question is indeed not clear. I assume lambdas are the only unknowns, i.e. volatility is given, dt = 1/ 12, and pu = pd = 0.5.
This gives you enough to calibrate lambda1, lambda2, ... , lambdaN so that the tree produces the start node = current one period rate (i.e. 1 month rate).
Having...
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