As U.S. stocks logged one of the most volatile days in recent weeks Tuesday, some investors positioned for bigger swings.

They turned to derivatives on the Cboe Volatility Index, or VIX, an options-based gauge of expected stock moves over the next month. At least one options investor dished out $4.3 million for bullish bets on the VIX that would pay out if the gauge jumped to 23 by October, a huge advance from its current level, according to data provider Trade Alert. Another large trade would pay out if the gauge jumped to...