Optimal Strategies of High Frequency Traders

This paper develops a continuous-time model of the optimal strategies of high-frequency traders (HFTs) to rationalize their pinging activities. Pinging, or the most aggressive fleeting orders, is defined as limit orders submitted inside the bid-ask spread that are cancelled shortly thereafter. The current worry is that HFTs utilize their speed advantage to ping inside the spread to manipulate the market. In contrast, the HFT in my model uses pinging to control inventory or to chase short-term price momentum without any learning or manipulative motives. I use historical message data to reconstruct limit order books, and characterize the HFT’s optimal strategies under the viscosity solution to my model. Implications on pinging activities from the model are then gauged against data. The result confirms that pinging is not necessarily manipulative and is rationalizable as part of the dynamic trading strategies of HFTs. A RECENT AND ONGOING heated debate concerns high-frequency traders and high-frequency trading activities (HFT stands for high-frequency trader/trading thereafter). The interest in this subject has grown significantly after the Flash Crash, because HFTs appear as a black-box mystery to the general public as well as to the academic world.1 One type of HFT activity that has attracted a great deal of attention due to HFTs’ speed advantage is the so-called pinging activity. Pinging, or the most aggressive fleeting order activity, is defined as the submission of ∗Bendheim Center for Finance, Princeton University. I am deeply indebted to Yacine Aït-Sahalia for his invaluable advice, frequent encouragement and numerous insights. I am also very grateful to Harrison Hong for his many suggestions. I also thank Valentin Haddad, Christopher Sims, David Sraer, Wei Xiong, as well as seminar participants at the Princeton Civitas Foundation finance seminar and the Princeton-QUT-SMU conference for helpful comments. 1For a comprehensive review of the Flash Crash, see the study by Kirilenko et. al. (2011). See also Easley et. al. (2011)’s examination on the same subject.