An automated stock exchange in which a computer matches buy and sell orders for a plurality of stocks. An open board simultaneous trading environment is simulated through two stages. The first stage is an order accumulation period which is continuously in operation except for one stock in the second stage. The second stage is an extremely rapid sequential call through. All orders for a given stock are available to customers during the first stage. During the second stage market orders are matched with market orders, then market orders are traded against limit orders as the trading price changes within controlled ranges. The system will also process stop orders, and other specialized transactions.