options on futures

hey, Does anyone know why it is that we use ft(T) when calculating the payoff of the option on a futures contract but we use f0(T) when calculating the lower bound of the options on futures? Thanks!

i don’t think this terminology is helping anyone…can you post a problem so we can think about it without the formulas…thanks

Are you referring to Put call partiy on futures? C + (X- F)/(1+RFR)^(t) = P ??

I hate that put call formula. It seems so needlessly complicated. Why not just say C + X/(1+RFR)^t = P + S I mean that really is the put call parity formula and it makes sense…fiduciary call = protective put. Then just use algebra to solve for whatever unknown they throw at you