When a company (the issuer) offers its securities for sale, there is a chance that the market might demand for more shares than are being offered. A green shoe option allows the issuing house (the investment bank managing the process) to sell additional shares thereby increasing the offer size without increasing the share price.
A reverse green shoe option is used when the market does not respond with enthusiasm. The offer might be undersubscribed or the share price might fall below the offer price after the shares are listed and available for trading. Such situations tarnish the reputations of both the issuer and the issuing house. A reverse green shoe option is a price support mechanism which is just a fancy way of saying market manipulation. It is the only market manipulation mechanism that is legal. When a reverse green shoe is implemented, the issuing house would buy shares from the market. The effect of this is to reduce the outstanding shares without reducing the share price.
This process is named after an American company called Green Shoe Manufacturing Ltd which was the first to use it in 1919.
My first experience of this was in 2008. I was working on an offer where a bank wanted to raise about $1 billion. In Nigeria, just like the US, the regulations limit the green shoe to 10%-15% of the original offer. This offer however, was over 200% oversubscribed. The period 2004 to 2008 was a fantastic time for finance in Nigeria. Banks exploded in size, the stock market broke records routinely and international money flowed in. In normal times, finance people are always pushing the boundaries of the law. In times of economic exuberance, the law is broken with the deliberate ignorance of the regulators. In the case of my offer, the issuer wanted to take the entire $2.12 billion that had been offered. Part of our job was to find a way around the SEC rules. We implemented the option for the allowable portion of the oversubscription and did a private placement for the rest. That entire transaction is one of the jobs I am most proud of. Unfortunately, the bank collapsed less than 5 years later due to the greed and mismanagement of its managing director.