From ACT Wiki
Securities issuance - price stabilisation.
A greenshoe option is an option granted by an offeror of securities in favour of the underwriters, investment firms or credit institutions involved in the offer for the purpose of covering overallotments.
Under the terms of the option, the underwriters - and sometimes others - may purchase up to a certain amount of relevant securities at the original offer price for a certain period of time after the offer of the relevant securities.
Also known as an over-allotment option.
The term ‘greenshoe’ derives from the option’s first use by the Green Shoe company in 1917-18.