If a company declares extra-ordinary dividend (i.e. greater than 5% of the price of the shares), the F&O contracts are adjusted by the exchange to incorporate the effect. In other words, the dividend amount is reduced from the price of futures and strike price of the options on the ex-date.
Check this circular from NSE on the adjustment of F&O contracts in ITC on the ex-date which is July 6th, 2020.
Adjustments for Futures Contracts:
Base price of the Futures contracts on July 06, 2020 will be reference rate less aggregate amount of
dividend i.e. Rs. 10.15/-. The reference rate to be reckoned for this purpose shall be the daily mark to
market settlement price of the relevant futures contract.
Assume you buy one lot of ITC futures on July 5th at Rs 205. The closing price for the day is Rs 208. In this case, you have made Rs 3 marked-to-market profit. On July 6th, the base price will be reduced to Rs 197.85 (i.e. 208 - 10.15). If the closing price is Rs 198 on that day then you have made a Rs 0.15 marked-to-market profit.
What this means is that the futures won’t trade at a discount to the spot price like when there is a normal dividend announced. On ex-dividend date, the futures price will be reduced by Rs 10.15.
Adjustments for Options Contracts:
The full value of dividend i.e. Rs. 10.15/- would be deducted from all the cum-dividend strike prices
on the ex-dividend date. The details of the old and corresponding new options contracts that shall be
available for trading from July 06, 2020 would be notified on July 03, 2020
For instance, the strike price of Rs 200 call option will be reduced to Rs 189.85 (i.e. 200 - 10.15) on July 6th.
The lot size of the F&O contracts will not change. Also, if you hold equity shares of ITC in your demat account as on July 5th, you will be entitled to receive the dividend. The equity share price should theoretically reduce by Rs 10.15 on July 6th.