Greenshoe - Issuer or underwriter's option?
I have read about this and am bit confused. Is this an option the issuer or the underwriter has? I also understand this is an option that can be exercised at listing or within 25 days.
Example: The stock rises after listing.
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If the issuer has the greenshoe option and the price rises after IPO: Would want to sell more shares to the public and buys these shares from the issuer at lower price. Books a profit. The company raises more capital and the amount of outstanding shares increase.
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If issuer has the greenshoe option and the price rises after IPO: Would not want to issue more shares at the IPO price, when the share price is already higher.
Is my understanding correct?