Somebody went out and bought 1,200 October calls at 18. That's on top of the 1,000+ open interest in August 15 calls. That October position cost $60,000 to put on and the open interest in the August 15 calls would cost $136,350 to put on, so that's not simply idle curiosity.
If Coty or Buffett were to go back to Avon at 22, the October call would suddenly be worth more than $480,000 and the August call would suddenly be worth more than $707,000. Options have an intrinsic value and a time value - the above would just be the intrinsic values for those options.
Avon has a number of hedge fund representatives on their board. I'm sure they've done this math as well along with what it might mean for their funds. They may have simply thought the offer was undertaken at a bad time for Avon with their stock down and might be waiting for the next quarterly report for the stock to come back up and then go for an offer significantly higher than 22.
It wasn't too long ago that this stock was at 30, they might be aiming to get the stock over 20 through some good turnaround signs and then take an offer at 30.
Then those options would be worth a whole lot more.
Disclosure: I have no positions in any stocks mentioned, but may initiate a long position in AVP over the next 72 hours.