Binomial Tree for options on futures

[unique]

It seems that when you find the option price of the future option using multi-period binomial tree , you have to pull back node by node since all future options are like american options and we cant pull back to C_0 from C_uuu
in one step because at the lower node C_uu it might be optimal to exercise the option and to pull back further we would need to use that exercise value and not the option value.
So on the exam it will take a lot of time and careful calculations to find C_0.

Is this a correct observation if not what it the faster way to get C_0 of the future option ?

[Actuarialsuck]

If your option isn't American then you can't exercise at intermediate nodes and you CAN pull back from the most outer node, you just have to account that for some nodes, there are multiple ways of getting there (think choose function).

[unique]

I know that.
My question was if there a shorter way to find the value of American or future option at time=0 without pulling back node by node.

[Force of Interest]

No there isnt. On the exam they might do something like say its American but that it doesnt pay div's. i.e. its still European, or at least the same price. You won't get something on the exam that will take forever to pull back through and check every node.

[unique]

thanks