The price of the digital currency bitcoin rose sharply on Monday with news that the U.S. is set to have its first regulated exchange.

San Francisco-based Coinbase offers storage services for bitcoin users, and the company is set to open a new exchange on Monday morning. Called Lunar, it will have regulatory approval in half of the states in the U.S., according to a report in The Wall Street Journal, including New York and California.

"A proper U.S. exchange that's trustworthy, that's insured, we were the first guys to get insurance on our bitcoin in some form, this will really help bring a dampening of volatility," said Coinbase co-founder Fred Ehrsam on CNBC's "Squawk on the Street." The company last week announced a major new round of funding and has now raised $106 million. The New York Stock Exchange and Spanish bank BBVA are just some of the company's high-profile backers, along with USAA bank, the investment arm of Japanese telecom NTT DoCoMo, and former Citigroup CEO Vikram Pandit. "I think the New York Stock Exchange sees this as an important trend," said Ehrsam. "Really, what's happening in the background is, you're seeing some hedge funds dip their toe into the water in bitcoin in increasing amounts. It wouldn't surprise me if you see some banks get involved here at some point, as well."

Bitcoin is a virtual currency that allows users to exchange online credits for goods and services. There is no central bank that issues them. Instead, bitcoins are created online using a computer to complete difficult tasks, in a process known as mining. The digital currency is renowned for its volatility and has been heavily criticized for facilitating illegal activity, given that it can be used anonymously.

Jeffrey Robinson, the author of "BitCon: The Naked Truth about Bitcoin" is one such notable critic. He told CNBC previously that he believed it was a "pretend currency masquerading as a pretend commodity." The insolvency of Japanese exchange Mt. Gox and the recent trading suspension at Bitstamp, the second-largest dollar-bitcoin exchange, has hurt the reputation of the cryptocurrency and has dented the price, which tanked by around 65 percent in 2014. Monday's news caused its value to spike, however, and is likely to inject some much-needed trust back into the digital currency. It saw a 16 percent jump on Monday morning and was trading close to $300 for one bitcoin, according to industry website CoinDesk. "To be clear, it's insurance against bitcoin loss," said Ehrsam "On top of the fact that we've been operating successfully in the U.S. for about 2 1/2 years, the largest bitcoin company has insurance to back it all up." This is important news for the U.S.-based exchange marketplace, according to Jon Matonis, the founding director of the Bitcoin Foundation, which is a not-for-profit organization which aims to promote and protect the cryptocurrency. "It will be a true floating-rate exchange with various order types," he told CNBC via email. "U.S.-based floating-rate exchanges contribute less than one percent to overall global trading volume for bitcoin, so I would expect that percentage to increase significantly."

The Bitcoin Center of New York City is seen on February 25, 2014 in New York City. The center operates as a physical place for people to come and trade digital currencies; there are over 100 digital currencies. Getty Images