For the second time in its history, digital payments company PayPal has gone public.

PayPal, which had its genesis as a scrappy startup that let consumers buy securely from smaller online merchants in 1998, was founded by now-famous tech luminaries and investors Peter Thiel, Elon Musk, and Max Levchin.

The company’s share price surged 11 percent on the NASDAQ Monday, reaching $42.55 by mid-day, before closing up 5.4 percent at $40.47. That intra-day high was more than triple its share price in February 2002, when the company first went public.

The company’s story is one that entrepreneurs will want to follow, as it’s a testament to the need to continue to innovate, transform, and sometimes bend to market exigencies.

“It’s fantastic to see PayPal back on the NASDAQ after 12 years,” said William Ready, PayPal’s global head of Merchant and NextGen Commerce at PayPal. “It’s worth more now and has the potential to fulfill the original vision of PayPal.”

At that time of its first public offering, PayPal was valued at $1.5 billion. When it was acquired in late 2002 by e-commerce company eBay, the move was seen as smart merger of two companies that were often rivals competing for merchants and online payment opportunities.

Today it’s a different story. PayPal is valued at $46 billion, while former parent Ebay is valued at about $34 billion. It has 169 million active customers, and works with more than 8 million merchants, facilitating transactions globally in 100 currencies. For the full year 2014, it processed $235 billion in transactions, of which 20 percent were mobile. Ebay and PayPal decided to split up last September.

Tough Terrain

While PayPal had a first mover advantage in online payments when it launched, it also competed with large banks and credit card companies such as Mastercard, Visa, and American Express. Today it goes head to head with a host of payments companies, both old and new, that are tackling the online transactions industry, including the burgeoning mobile payments world. Competitors include Square and Stripe, a 2015 Inc. 30 Under 30 company.

PayPal will also compete with tech titans Apple and Google, whose digital wallets allow consumers to purchase products and services using iOS and Android smartphones. And for that reason, it must continue to innovate.

“Mobile and online commerce is where PayPal has made the largest gains. As they continue to address the online marketplace and add in other features, they have a great chance to make headway,” says Madeline Aufseeser, a senior analyst with financial industry research firm Aite Group.

One example of how PayPal has innovated in recent years, is through its introduction of a payment option at the register for some bricks and mortar merchants, such as Home Depot.

Room to Grow

Yet the market for transactions of all kinds is a huge one, and has the potential for rapid growth for any innovative payment company. Annual credit card sales are worth about $12 trillion, and e-commerce sales clock in at about 10 percent of all retail sales. For its part, PayPal has captured about 30 percent of U.S. e-commerce sales, according to CEB TowerGroup.

“It’s a wonderful move for PayPal and shows the value of the industry since eBay acquired it,” says Brian Riley, a principal for CEB TowerGroup. “There is a tremendous depth to the industry for payments and retail transactions.”

In recent years, PayPal has been an active acquirer of promising payments startups, and that’s a trend that’s likely to continue, says Gil Luria, managing director for Wedbush Securities. In 2013 in a deal worth $800 million, PayPal acquired online payment gateway Braintree, of which Ready was chief executive. In early July, in a deal worth $1 billion, it acquired Xoom, which enables international money transfers digitally. This spring it also acquired a mobile payments company called Paydiant for $280 million.

“PayPal is now the preferred exit for most new payment companies,” Luria said.

And for one of the company’s founder, the launching of the newly public PayPal was a validation, as well as hope for greater things.

“It’s pretty awesome to see our collective baby all grown up and going off into the real world,” Max Levchin said by instant message on Twitter. “[I] hope they take some real risks!”