Abstract
This paper provides a mathematical analysis of how high frequency traders profi t from their speed with respect to the limit order book. We show that their pro ts can be decomposed into two components. The rest 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 profi ts 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 to the efficient functioning of financial markets.
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