New European capital Solvency II rules introduced in January require insurers to account for investment risk, and solvency models to be regularly updated.
Life insurers in particular invest in bond markets to match their long-term pension liabilities, and have increasingly moved into corporate bond markets which offer higher returns.
But confidence in UK corporate bonds is dipping and equity markets, in which insurers also invest, are weaker too.
"It is the market moves that are having the more significant impact. Solvency II models are sensitive to moves in credit spreads, equity markets, FX, interest rates, property prices and other markets," said Marcus Rivaldi, deputy head of analytics at specialist insurance investment manager Twelve Capital.
"The impact on the day-to-day operations of insurance companies in the UK should be relatively minimal," he said.
Legal & General (>> Legal & General Group Plc), which reassured investors earlier this year that it was not holding many junk energy bonds, was the worst performing FTSE 100 insurer on Monday.
It has lost nearly 30 percent of its value since Thursday's close and was trading at three-year lows at 166 pence at 1400 GMT.
Legal & General's solvency ratio would drop to 158 percent if there is a fall in interest rates after a Brexit vote, from 169 percent reported at end-December, ratings agency Moody's estimated last month.
Analysts at JP Morgan estimated L&G's solvency ratio currently at 150 percent.
A ratio of 100 percent means insurers have enough capital to cover underwriting, investment and operational risks, but some analysts think life insurers should have a ratio of as much as 160 percent, given their long-dated liabilities.
"If the volatility continues then we believe that Prudential (>> Prudential plc), Legal & General (>> Legal & General Group Plc) and JRP (>> JRP Group PLC) would struggle on capital," JP Morgan said in a note.
Prudential's shares have dropped nearly 20 percent since the vote, and mid-cap insurer JRP is down 35 percent.
Legal & General also invests heavily in UK property, a sector that has taken the largest drubbing since the vote.
Aviva (>> Aviva plc), which fell as much as 30 percent at one point on Friday to its lowest in nearly four years, said on Monday its capital position was resilient.
Shares in Aviva, which has a target range for its solvency ratio of 150-180 percent, rose briefly at the open, and analysts at Macquarie said the sell-off was overdone. But it quickly reversed and was down 7.4 percent to 346.8 pence by 1405 GMT.
Ratings agency Fitch warned on Friday that life insurers were at risk of downgrades if there was "sustained economic weakness leading to intensified competition and material deterioration in the market values of assets".
However, some investors and analysts were more upbeat, saying the lower pound could be a boon for some insurers, boosting earnings from overseas operations.
"In situations like this, there are often opportunities," said Nick Martin, who runs an insurance fund for Polar Capital.
(Additional reporting by Simon Jessop; Editing by Sinead Cruise and Alexander Smith)
By Carolyn Cohn