Whwn the MM prices the Puts they include the dividend in the ATM and higher Puts for those contract months which are in the future, which will contain X number of dividends. The MM's are thinking(IMO) a 1.00 dividend going forward, so 15Jan 32Puts are priced at 10.50 because they contain 9 dividends(1.00 x 9) + 1.50(difference in today's PPS and 32.00).
Now, my original post meant that when the MM's sell that 15Jan32PUT @ 10.50 to the Long Put holder, they simultaneously short the corresponding number of shares @ market to hedge their position. They have to pay the dividend on their short share hedge and that is why they increase the price of the Puts(to the Long Put purchaser), in order to cover that cost.
Likewise, when I short that Put, they buy the corresponding number of shares to hedge my short position. EX gets placed after the OPEX and the 32Puts lose 1.25 in value. The MM paid 1.25 more than he had to and he has no value in the Long shares to get it back. IOW, if he thought the EX would be after OPEX he would have paid 1.25 less for the Puts. Now he does not get the 1.25 dividend on the expiring option he bought from me, because the options expire before EX. He is SOL and out the dividend for Dec that was originally in the Put he bought from me.
That is a long explanation and I was waiting for the person(you...;-)) to ask how the MM's get raked over, when they have bet already on the EX being pre OPEX, and then the EX is placed post OPEX.
AFAIK the option MMs try to stay delta neutral so they wouldn't be long or short the full number of shares (i.e. they would be 100*delta per contract). Plus they would offload the options as soon as they could, they don't keep options or stock in their inventory if they don't have to.
MMs do indeed try to be delta neutral -- and their main tool for accomplishing this is to offset net option delta exposure with long or short shares.
But even though their net option delta may be small (because they have bought and sold puts as well as calls), pricing has to be set the way Doc described to eliminate arbitrage opportunities in the market. If the put prices did not include the expected dividends for the life of the put (modulated by delta), then everybody and their brother would be buying shares and protecting them with cheap ITM puts and would then be able to sit back and collect the dividends risk-free.
As nature abhors a vacuum, so the market abhors arbitrage, and the put prices must include the (expected) dividends.