High Frequency Traders and Asset Prices

Do high frequency traders affect transaction prices? In this paper we derive distributions of transaction prices in limit order markets populated by low frequency traders (humans) before and after the entrance of a high frequency trader (machine). We find that the presence of a machine is likely to change the average transaction price, even in the absence of new information. We also find that in a market with a high frequency trader, the distribution of transaction prices has more mass around the center and thinner far tails. With a machine, mean intertrade duration decreases in proportion to the increase in the ratio of the human order arrival rates with and without the presence of the machine; trading volume goes up by the same rate. We show that the machine makes positive expected profits by "sniping" out human orders somewhat away from the front of the book. This explains the shape of the transaction price density. In fact, we show that in a special case, the faster humans submit and vary their orders, the more profits the machine makes