IPO questions : price discovery & greenshoe

Hi,

quick questions for the ECM guys lurking here :)

how is price discovery acheived before an IPO? (valuation done by the underwritter, then roadshow/bookbuilding then final fine tuning ahead of hte IPO itself?)
who provides the extra shares for the greenshoe? (company or shareholders? -I read "promoters" a few times and I am not sure who benefits from this)
Do owners cash out / profit from the greenshoe?
Does Stabilizing Agent get to profit from selling the shares at IPO price and buying them back below IPO price in case it has to support the share price? or are the share bought back on the market just returned to the company/shareholders?

Thanks much!

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IPO questions : price discovery & greenshoe

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