Book Building 

To estimate demand and pricing for an initial public offering (IPO) or other securities issues, corporations employ a process known as book building.

The firm's underwriter (often an investment bank) collaborates with the company during book building to establish the best price range for the securities being issued, taking into account the market environment, the company's financial performance, and other elements. In order to determine the demand for the securities, the underwriter then reaches out to institutional investors including hedge funds, mutual funds, and pension funds.

The underwriter compiles this information into an order book or "book of demand," which shows the quantity of securities that each investor is willing to buy at various prices within the price range. The underwriter uses the book of demand to determine the final offering price for the securities, which is usually set at the highest price that will still attract sufficient demand. The underwriter's goal is to set a price that will attract sufficient demand to sell all of the securities being offered, while also maximizing the price per security. The final price is typically set at the highest price that will still attract sufficient demand to sell the entire offering.

Book building allows companies to get a better sense of the demand for their securities and helps them determine the best price for the offering. It also allows institutional investors to participate in the IPO or offering at a lower price than they might otherwise be able to obtain, since they are buying directly from the company rather than in the open market.

The underwriters may also use statistical and analytical models to assist with the pricing decision. For example, they may use regression analysis to estimate the relationship between the offering price and demand for the securities, based on past data. However, the ultimate pricing decision is usually based on a combination of quantitative and qualitative factors, rather than a specific formula.

Some key factors that underwriters and issuers consider when pricing a securities offering:

Company financials: 

The financial health and future growth prospects of the company can affect the demand for its securities.

Market conditions: 

The overall state of the market can also impact the demand for a securities offering.

Comparable companies: 

The pricing of the securities offered by the company is often compared to other companies in the same industry.

Investor demand: 

The level of interest shown by potential investors is a key factor in determining the final price of the securities.