Shares in PayPal jumped Monday in the first day after being spun off by eBay, with the online payments group seeing a market value higher than its former parent.

At the closing bell on the Nasdaq exchange, PayPal was up 5.42 percent at $40.47, equating to a market capitalization of more than $49 billion. The share price rose another percent in after-market trades.

Meanwhile, eBay rose 2.4 percent to $28.57, giving the auction giant a value of some $34 billion at the end of formal trading for the day but the share price slipped slightly to $28.38 after the market closed.

"We are excited to celebrate our listing day and embark on our next chapter,” PayPal chief executive Dan Schulman said in a release.

"As an independent company, we see a tremendous opportunity for PayPal to expand our role as a champion for consumers and partner to merchants, and to help shape the industry as money becomes digital at an increasingly rapid pace."

Analysts at BMO Capital Markets said PayPal is a "unique" opportunity for investors because it has the potential to disrupt the market for personal and online payments.

BMO analyst Paul Condra, in a note to clients, called PayPal the "only truly disruptive consumer payment network with scale and strong brand recognition."

He said it was "uniquely positioned not only as a beneficiary of growth in electronic payments but also as a quasi-disruptor of the incumbent card-based systems (MasterCard/Visa)."

The spinoff, announced last year, came after months of pressure from activist investor Carl Icahn, who had assailed eBay for poor management and claimed that keeping eBay tied with PayPal depressed the value of both units.

eBay acquired PayPal in 2002 for roughly $1.5 billion in shares, integrating the payment service that had already been widely used for online auctions. PayPal had traded on the Nasdaq exchange prior to being acquired by eBay.