When an initial public offer is issued and it is listed below the the real value of stock. When the stock is listed into the market and its closing price on the first day exceeds the price at which the share was issued at, this scenario is said to be under pricing.
Underwriting is the process of giving a guarantee to the company that underwriters in case the shares are not fully subscribed the public,investment bank will subscribe them.
Investment bank can also gain on these underpriced issue if the shares were not fully subscribed by the public and if it is listed above the price and it's closing above the listing price in such case the underwriters will gain a fair chunk of money.
Underwriters look for always listing the shares at premium to the issue price because in such case there seems to create the value for the new potential investors and it is good for the reputation of the underwriters as they help in getting new potential investors for the long term. It can also create negative for the venture holders who are offloading their share in the public offer.
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