The recent market rout caught some star Wall Street traders by surprise. But not a hedge-fund firm affiliated with “The Black Swan” author Nassim Nicholas Taleb, which gained more than $1 billion on a strategy that seeks to profit from extreme events in financial markets.

Universa Investments LP was up roughly 20% on Monday, according to a person familiar with the matter, a day when the Dow Jones Industrial Average collapsed more than 1,000 points in its largest intraday point decline. The blue-chip index finished down 588...