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Betting exchange Betfair showed odds of around 15 percent for a vote to leave, down from more than 40 percent a week ago before the killing of British lawmaker Jo Cox.
The pound gained 1.2 percent on the day to as high as $1.4889 before pulling back to $1.4855.
One-month implied volatility of sterling, shown in prices of currency options, fell to around 19 percent from 25 percent on Wednesday, also an indicator of a drop in the chances of extreme moves in the pound over the next 24 hours.