Analysts at Oxford Economics said market behaviour over the last few weeks in response the the swinging fortunes of both sides could be just a sign of things to come after the vote.
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"The scale of recent market moves rather suggests markets are pricing in quite a high risk of an extreme 'Lehman Brothers'-style outcome from Brexit," a report from the group said.
They added: "It's hard to square such moves with a debate over whether the UK economy - only 3.5 per cent of world output - may be a few per cent bigger or smaller in 10 to 15 years time."
The FTSE 100 jumped three per cent yesterday while sterling experienced its biggest daily climb since the financial crisis as a number of polls showed support edging back to the Remain side.
Analysts and traders from a host of organisations have warned that this week will be one of the most volatile since the downturn with investors on edge and markets highly susceptible to move markets on the smallest piece of referendum news.
However, such moves could be "overdone" according to Oxford Economics. They predict a fall in the value of sterling of around nine per cent immediately after a vote to Leave, but expect the currency to recovery after this overreaction.
"Our modelling and analysis suggests sterling would be likely to rally after an initial sell-off", researchers said, adding that a weaker sterling was a "potential positive for UK stock indices" since up to 80 per cent of the FTSE 100's earnings come from overseas.
The FTSE 100 and the pound largely held on to yesterday's gains in early morning trading. The bluechip index was down 0.3 per cent at 6,186, while sterling was up 0.2 per cent at $1.4721.