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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

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Are you referring to Put call partiy on futures?

C + (X- F)/(1+RFR)^(t) = P ??

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