SIGEST

Abstract

The SIGEST article in this issue is “Algorithmic Trading, Stochastic Control, and Mutually Exciting Processes,” by Álvaro Cartea, Sebastian Jaimungal, and Jason Ricci. The article first appeared in the SIAM Journal on Financial Mathematics in 2014, under the title “Buy Low, Sell High: A High Frequency Trading Perspective.” In preparing this SIGEST version, the authors have - updated Figure 1 with data from 2018; - added section 7 on follow-up work; - edited some text in order to reflect current market conditions; - trimmed section 6 of some technical material; and - updated the references. The first section of the article gives an accessible introduction to the world of electronic markets, where events take place on a microsecond timescale. The authors explain the key concepts of algorithmic trading, high frequency trading, limit order markets, the limit order book, a best bid, a market order, and an influential/noninfluential order. In modern markets, liquidity provision---making sure that buyers and sellers are readily available---relies increasingly on the presence of high frequency market makers. This work develops strategies that these players can use to survive and flourish. A major aim of the work is to extend existing optimal market making frameworks by including a structural model of market order dynamics, inspired by Hawkes processes, and mean-reverting midprice moves. (The midprice is halfway between the best offer and the best bid.) In this model, the market maker has access to a short term prediction of the midprice and can use limit orders to buy and sell continuously during the day. Here, it is crucial both to provide liquidity and to guard against adverse selection by using the prediction of the future midprice. To make progress, the authors extend an approach that they had already used successfully on an optimal execution problem: replace the usual risk aversion term (the square of a position in dollars) by a risk aversion in shares. In this way, the problem can be tackled explicitly using stochastic control techniques. Simulations are given that emphasize the advantages of the resulting optimal trading strategy. Overall, this work shows how modeling, analysis, and computation can impact the fast-moving world of high frequency trading.