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You get nothing, by this logic you could accumulate risk-free money all day by buying/selling on the ex-date as long as the dividend is larger than the spread.


1

You could compute index dividend yield from ATM options using linearized put-call parity (assuming index options are European.) The present value of the dividend payment is: $PV(div) = P - C + (S - K) + K(e^{rT} - 1)$ where $r$ is interest rate to the option expiration and $T$ is time to maturity in years. Then the implied dividend is: $d = ...



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