PayPal President and CEO designee Dan Schulman speaks during an event at Terra Gallery in San Francisco, California May 21, 2015. REUTERS/Robert Galbraith

PayPal is its own company again. The payment firm, which officially spun off from eBay last week, started trading under the "PYPL" ticker Monday on the Nasdaq exchange, and closed the day slightly up at a price of $40.47 per share.

That put its market capitalization -- the price per share multiplied by the number of outstanding shares -- at $47.13 billion at market close, though its value Monday was as high as $49.5 billion. As Business Insider noted, that's far more than it's former parent company -- which now has a value of $34.7 billion -- and also makes it larger than Twitter, which has a value of roughly $23.4 billion. It's roughly the same size as Netflix, which closed Monday with a market cap of $48.7 billion.

It was a solid debut for the firm, which decided to return to the same ticker symbol it used on the Nasdaq exchange before its 2002 eBay acquisition.

After more than 12 years as a part of eBay, PayPal is in a strong position when it comes to several online payment trends. That's due not only to the success of the traditional PayPal service, but also to its business-focused branch Braintree and the peer-to-peer payments app Venmo. The company also recently announced that it has acquired Xoom, an online money transfer company. But the space is a crowded one, with startups such as Square and traditional companies such as Visa, Apple and Google eyeing a way to become the method of choice for online payments.

To get ahead, PayPal chief executive Dan Schulman said the company will continue to build its products but also work to break into underserved markets, where there isn't basic financial infrastructure.

"[We’ll] work with people around the world to make financial services accessible and affordable to everyone, anywhere in the world, so that it is simpler, safer and cheaper to spend, save, manage and move money than it has ever been before," Schulman said in a company blog post.