Apollo Global Management is using fancy footwork to get one of the biggest leveraged buyouts in years through an increasingly jittery debt market.

The private-equity firm said on February 16 that it has agreed to buy ADT Corp in a deal that values the burglar-alarm vendor at about $7 billion. It comes at a time when falling oil prices and concerns about a global economic slowdown have soured banks and many investors on the junk-rated debt used to back leveraged buyouts.