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Given an option on an underlying future, where the option matures at $T_1$ and the future matures at $T_2$, and $T_2 > T_1$, when priced using the Black76 formula, what is $F$?

Is it just the current futures price $F(T_2)$? Or do we need to compute some sort of estimate of what the futures price $F(T_2)$ is seen from point $T_1$? And if so, how do we do that?

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    $\begingroup$ Futures contracts are marked to market. Therefore, the payoff is realized when the option is exercised. Your consideration plays a role with forwards, as shown here. $\endgroup$
    – AKdemy
    Feb 2 at 13:16
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    $\begingroup$ If for example you have May 2024 S&P Futures options, where the underlying is June 2024 S&P Futures (May S&P Futures do not exist). Then I believe in the Black formula you would use T for the third friday in May but F for the June futures. $\endgroup$
    – nbbo2
    Feb 2 at 13:58

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