Say company X has a share price of $80. They think their shares are undervalued, and their board approved a buyback of $1 billion. Can company X use the $1 billion to sell puts at $79, with the idea that if the price drops they buy back at cheaper than current market price, while if the price doesn't drop they make a profit and can sell puts again in the future?
I've seen no mention of this method of buybacks anywhere, but it seems to make sense. After all, both results are good for the company. The latter result (the share price goes up) doesn't result in an actual reduction in float, but it does result in a profit, and presumably shareholders won't mind. Is this already being done? If not, why not? Only thing I can think of is that it's illegal, but I don't see why.