Liquidity Suppliers and High Frequency Trading

This paper provides a mathematical analysis of how high frequency traders profit from their speed with respect to the limit order book. We show that their profits can be decomposed into two components. The first is due to their ability to execute market orders at limit order prices and without incurring any liquidity costs themselves. The second is by "front running" market orders with limit prices. These trading profits are shown to be at the expense of ordinary traders who submit market orders and sophisticated traders who submit limit orders or who use algorithmic trading to split up and execute large trades. We do not consider the welfare implications of our insights for the efficient functioning of financial markets.