I think this is a very interesting question and I am glad you pointed out the mistake I made. Our office suite is inside the FIMAT clearing office here in Philly, so before the bell I took a quick informal and unscientific poll of about a dozen market makers before then went down to the floor. Itâs been a number of years since I was down on the floor trading. Hands down not one of the dozen said they would even early exercise a deep put where the call was no bid at a nickel. For the most part they all concur with your math, or their firms do but theyâre not sellers of the call at zero basically. Both of the âlocalsâ of which there are very few who make their own decisions on early ex didnât give it a second thought and the rest of the guys who were essentially box monkeys for huge firms and donât make the early ex decision for the firm mentioned their firms virtually never early ex any puts. The only caveat any of them mentioned were the guys in the SOX index which is a cash settled American style option, so when you exercise deep puts your net delta the next day is longer for each put or shorter for each call you early ex.
Again, thanks for the correction on hard to borrow, itâs a HUGE issue for the reasons you mentioned on having your short stock called in. This is an interesting dialog.