Joanne Lipman of the Institute for Advanced Study and Alex Kantrowitz of Big Technology join CNBC's "Squawk Box" team to break down Palantir's stock market debut. For access to live and exclusive video from CNBC subscribe to CNBC PRO: https://cnb.cx/2NGeIvi

Palantir shares opened at $10 on Wednesday in the company’s debut on the New York Stock Exchange, and closed the trading session at $9.50.

Palantir, which develops data analysis software for government agencies and large companies, held a direct listing of its stock, giving existing shareholders the opportunity to sell up to 20% of their stake to new investors. Cloud software developer Asana also went public via direct listing on Wednesday.

The initial price gives Palantir a market cap of $16.5 billion, based on 1.65 billion shares outstanding, which excludes various restricted stock units (RSUs), options and unvested stock. The fully diluted share count is 2.17 billion, so Palantir’s stock market value will rise significantly as options, RSUs and unvested units convert to common stock.

Shares of Palantir, founded in 2003, have been widely traded on the private market for years, though the company has struggled to maintain the $20.4 billion valuation from a 2015 financing round. The stock at that time was valued at $11.38 and traded this year for between $4.17 and $11.50.

The NYSE gave a reference price on Tuesday of $7.25 a share, though no stock changed hands at that level. It traded as high as $11.42 on Wednesday before dropping below its opening price. Some current and former employees complained early in the trading session of being unable to access the system to sell their stock.

Palantir has sparked controversy for its willingness to do business with agencies like U.S Immigration and Customs Enforcement and for a governance structure that gives co-founders Peter Thiel, CEO Alex Karp and Stephen Cohen a third class of stock with outsized control. The company is a creation of Silicon Valley, but has tried to distance itself from the region by moving its headquarters to Colorado and slamming tech’s “engineering elite” in its prospectus.

“Software projects with our nation’s defense and intelligence agencies, whose missions are to keep us safe, have become controversial, while companies built on advertising dollars are commonplace,” Karp wrote in the filing.

Karp’s letter was a less-than-subtle jab at Facebook, where Thiel made much of his fortune and still sits on the board. Through his various investing entities, Thiel is Palantir’s largest shareholder.

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