What is the greenshoe (over-allotment option) and how does it work mechanically?

The greenshoe is an over-allotment option (typically up to 15% of the base deal) that lets underwriters sell more shares than the base offering and is used as a price-stabilization tool. Mechanically: the syndicate over-allots by selling ~15% more shares than planned, leaving them short. If the stock trades DOWN below the offer price, they buy shares in the open market to cover the short — this buying supports (stabilizes) the price — and the option goes unexercised. If the stock trades UP, they can't buy cheaply, so they exercise the greenshoe to buy shares from the company/selling holders at the offer price to cover the short. Either way the bank is covered; the greenshoe lets them stabilize without taking directional risk.