Volatility has reawakened in the $5.1 trillion foreign-exchange market as traders start to imagine life without ultra-easy monetary policy.

The impact is greatest in the currencies with most at stake from an end to years where stimulus only got more generous—the so-called high yielders. A gauge of expected swings in emerging-market currencies has surged above an equivalent measure for developed markets by the most since May.

European Central Bank President Mario Draghi this month downplayed the need for an expansion of quantitative easing, while speculation has grown that the Bank of Japan could scale back longer-term bond purchases. Traders see better-than-even odds of higher U.S. interest rates by year-end.