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I have a question regarding the BS 1976 formula for futures options.

https://www.glynholton.com/notes/black_1976/

How do I deal with dividends under this model, assuming that the dividend yield is continously compunded? Background is that I want to model the implied volatility of options on index futures given a deterministic continously compounded dividend yield!

Thank you very much in advance,

Best regards,

John

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For most index futures I am familiar with (for example S&P 500 futures) the holder of the future does NOT receive the dividends. The interest rate $r$ and the dividend rate $d$ on the cash index determine the relationship between the future $F$ and the spot $S$ (i.e. $F= S e^{(r-d)T}$).

The Black 1976 formula for options on futures is based on F, the observable future price, and since the future does not receive the dividend there is no need for a dividend adjustment in that formula.

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