Uncertain Execution in Order-Driven Markets

Abstract

So-called `latency' refers to the various small but significant time delays that occur in the course of the communications between a trader and a market. Such delays happen between the time an exchange streams market data to a trader, the time at which the trader processes the information and decides to trade, and the time at which the exchange receives and processes the order from the trader. Latency is a challenge faced by all traders and is of great importance in modern financial markets. In the present work, we develop mathematical models to solve a variety of problems faced by liquidity takers regarding uncertainty in executions. Firstly, we devise a model for computing the price that traders are willing to pay to reduce their latency. This latency-optimal strategy balances the tradeoff, over a period of time, between the costs of walking the limit order book and the percentage of orders filled. This work may lead to social benefits, since it offers a way to stop the arms race to being faster in the marketplace. Secondly, we develop a latency-optimal trading strategy that improves the marksmanship of liquidity takers. We make use of the techniques of variational analysis to obtain the optimal price limit of each marketable limit order (MLO) that the trader sends. The price limit of each MLO is characterized as the solution to a new class of forward-backward stochastic differential equations (FBSDEs) driven by random measures. We prove the existence and uniqueness of the FBSDE solution and solve the FBSDE numerically to illustrate the performance of the strategies.\ Finally, we show how traders can optimally liquidate a position over a trading window when there is latency in the marketplace. We frame our model as an impulse control problem with stochastic delay -- this work contributes to the stochastic control literature by allowing one to have random delays before the impulses take place. We show that impatient liquidity takers submit MLOs that may walk the book (capped by the limit price) to increase the probability of filling the trades. Patient traders who are fast do not use their speed to hit the quotes they observe, nor to finish the execution programme early: they use speed to complete the execution with as many speculative MLOs as possible. We use foreign exchange data to implement the random-latency-optimal strategy and to compare it with various benchmarks. We find that for patient traders, the random-latency optimal strategy outperforms the bechmarks that do not account for latency by a quantity that is greater than the transaction costs paid by liquidity takers. Around news announcements, the value of the outperformance significantly increases. The superiority of the latency-optimal strategies is due to both the speculative MLOs that are filled and the price protection of the MLOs.