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EBay Inc. rose 4.9 percent to an almost eight-year high on optimism that it will benefit from a surge in online shopping ahead of the year-end holidays.

Shares of EBay, the biggest online marketplace, rose to $51.40 in New York, the highest closing price since Jan. 19,

2005. Amazon.com Inc., the largest Internet retailer, gained 1.6 percent to $243.62.

Consumers seeking to save time and money by doing their gift-buying over the Web are flocking to EBay on so-called Cyber Monday, when many retailers mark down items sold online. Sales volume for San Jose, California-based EBay was up 57 percent as of early today, a fivefold increase from last year, according to ChannelAdvisor, which tracks online commerce.

“EBay is definitely participating in holiday 2012 in a much different and larger way than last year,” Scot Wingo, ChannelAdvisor’s chief executive officer, wrote in a blog post today.

EBay and Amazon both have recorded strong sales gains each day starting with Thanksgiving, ChannelAdvisor said. Transactions on mobile devices have accounted for more than 30 percent of the total each day, the Morrisville, North Carolina-based tracking company said.

Victor Anthony, an analyst at Topeka Capital Markets Inc., and Gene Munster, an analyst at Piper Jaffray & Co., released positive research notes based on online sales data from ChannelAdvisor and ComScore Inc.

EBay is an investor in ChannelAdvisor, according to the company’s blog.

(Updates with closing shares in second paragraph.)