Hartford was among the most vulnerable insurers on the guarantees because the company didn't hedge risks as much as MetLife Inc. and Prudential Financial Inc., the largest U.S. life insurers, Devlin said by phone from London.

Liabilities on the contracts swelled in the financial crisis, helping drive Hartford to a U.S. bailout and fueling a 60 percent plunge in the Standard and Poor's 500 Life & Health Insurance Index in the 12 months ended May 3, 2009. It was that day that Buffett, at a press conference in Omaha, Nebraska, said the industry took on an "ungodly amount" of risk.

'That's Poison'

When insurers "tell the policyholder that he gets some of the up side and you take all the down side, that's poison," Buffett said. "That would be like a stockbroker telling you that he'll pay you back if your stocks lose money."

About 26,000 contract holders will get the Axa Equitable offer, scheduled to be mailed starting in October, Tizzano said.

"We are making this offer because high market volatility, declines in the equity markets, and the low interest-rate environment make continuing to provide these guaranteed benefits costly," Axa Equitable said in a June 8 regulatory filing.

Transamerica, a unit of The Hague-based Aegon, is offering a lump-sum option that was initiated in May, Cindy Nodorft, a spokeswoman for the company, said in an e-mail. The offering applies to eligible owners of Transamerica variable annuity policies with riders such as a guaranteed minimum income benefit, according to a company document.

Crystalizing Losses

While buying out customers may limit companies' gains from stock-market rebounds, insurers can still benefit from terminating their obligations, Atlantic Equities's Devlin said.

With lump-sum payments, "you crystallize some of the loss, but not all of it, and it frees up capital," Devlin said. Insurers "obviously design it in order to make sense for them."

Consumers will have to weigh contract terms, their health and other assets when deciding whether to take a lump sum, said Glenn Daily, a fee-only insurance consultant based in New York.