Affiliations: [a] Sloan School of Management, Massachusetts Institute of Technology, Cambridge, MA 02142-1347, USA; E-mail: firstname.lastname@example.org | [b] Department of Industrial and Enterprise Systems Engineering and Department of Mathematics, University of Illinois at Urbana--Champaign, Urbana, IL 61801, USA; E-mail: email@example.com | [c] E-mail: firstname.lastname@example.org
Corresponding author: Richard Sowers. R.S. was supported by NSF EFRI 1024837 during the preparation of this work. R.S. would also like to thank the organizers of the 2011 Ascona Seminar on Stochastic Analysis, Random Fields, and Applications for an atmosphere which facilitated the development of a number of the detailed calculations of Section 4.
The views expressed here are not necessarily those of the Commodity Futures Trading Commission.
Abstract: We propose and study a stylization of high frequency trading (HFT). Our interest is an order book which consists of orders from slow liquidity traders and orders from high-frequency traders. We would like to frame a model which is amenable to the (seemingly natural) mathematical toolkit of separation of scales and which can be used to address some of the larger issues involved in HFT. The main issue to which we address our model is volatility. An important question is how volatility is affected by HFT. In our stylized model, we show how HFT increases volatility, and can quantify this effect as a function of the parameters in our model and the separation of scales.