Crude oil bounced back Thursday after hitting multiyear lows this week, gaining more than 8 percent. Following the jump, energy stocks rose, leading gains for the .
Still, the 20 percent tumble in energy stocks this year has some traders worried about big oil companies and their dividends, Brian Stutland of Equity Armor Investments said.
"The farther they fall, the more players in the options market say, 'Hey, the dividends are going to get cut on these names,'" Stutland said Wednesday on CNBC's "Fast Money." "Don't think you just jump in on these stocks and go ahead and buy them because their yields are looking cheap."
According to Stutland, options traders are expecting a dividend cut of at least 10 percent for three big oil names over the next year and a half. Based on the prices of long-term options, Stutland said traders see ConocoPhillips, BP and Occidental cutting their dividends by 18, 15 and 10 percent respectively.
"We expect that ConocoPhillips will continue generating negative cash flow through 2017, with weak commodity prices compounding the pressures of high capital spending and a high dividend payout," Moody's Gretchen French wrote in a Thursday note.
But other analysts have high hopes for some of these names, such as Occidental.
"It has raised its dividend for 13 straight years and has paid a quarterly dividend continuously since 1975," Michael Burke of Argus Research wrote last week. "We believe that OXY can further curtail spending in order to preserve its dividend."
A ConocoPhillips representative said in an email to CNBC, "We have been crystal clear that the first priority use of cash is the pay the dividend." BP said the company does not comment on market rumors or speculation, and Occidental did not provide comment.