The future of the New York Stock Exchange is inside the redbrick building that is rising from the ground here about 35 miles from Wall Street.

Right now, the mammoth facility being constructed on the site of an old quarry is a largely empty shell with a jumble of high-tech gear. In about a year, the building is expected to house several football fields of cutting-edge computing equipment for hedge funds and other firms that engage in high-frequency trading, or the use of computers and complex algorithms to trade at lightning speed.