Initial Public Offering (IPO) Process
There are no "rules" about how the price should act after an IPO, so there are no guarantee that a "pop" would appear at the opening day.
But when an IPO is done, it's typically underpriced.
On average, the shares are 10% up at the end of the first day after the IPO (I don't have the source that, I just remember that from some finance course).
Also, after the IPO, the underwriter can be asked to support the trading of the share for a certain period of time.
That is the so called stabilizing agent.
They have few obligations like:
- Providing liquidity to avoid strong price movement.
- Supporting the price by buying the share below a certain level.
This price support in often done by a repurchase of some of the shares of poorly performing IPO.
EDIT: Informations about the overallotment pool.
When the IPO is done, a certain number of client buy the shares issued by the company.
The underwriter, with the clients, can decide to create an overallotment pool, where the clients would get a little more shares (hence "overallotment"), but this time the shares are not issued by the company but by the underwriter.
To put it another way, the underwriter oversell and becomes short by a certain number of shares (limited to 15% of the IPO).
In exchange for the risk taken by this overallotment, the underwriter gets a greenshoe option from the clients, that will allows the underwriter to buy back the oversold shares, at the price of the IPO, from the clients.
The idea behind this option is to avoid a market exposure for the underwriter.
So, after the IPO:
If the price goes down, the underwriter buys back on the market the overshorted shares and makes a profits.
If the price goes up, the company exercise the greenshoe option buy the shares at the IPO prices (throught the overallotment pool, that is, the additional shares that the clients wanted ) to avoid suffering a loss.