Optimal Decisions in a Time Priority Queue

Abstract

We show how the position of a limit order in the queue influences the decision of whether to cancel the order or let it rest. Using ultra high-frequency data from the Nasdaq exchange, we perform empirical analysis on various limit order book events and propose novel ways for modelling some of these events, including cancellation of limit orders in various positions and size of market orders. Based on our empirical findings, we develop a queuing model that captures stylized facts on the data. This model includes a distinct feature which allows for a potentially random effect due to the agent's impulse control. We apply the queuing model in an algorithmic trading setting by considering an agent maximizing her expected utility through placing and cancelling of limit orders. The agent's optimal strategy is presented after calibrating the model to real data. A simulation study shows that for the same level of standard deviation of terminal wealth, the optimal strategy has a 2.5% higher mean compared to a strategy which ignores the effect of position; or a 8.8% lower standard deviation for the same level of mean. This extra gain stems from posting a limit order during adverse conditions and obtaining a good queue position before conditions become favourable.

Keywords: algorithmic trading, high frequency trading, limit order book, queuing model, order flow, impulse control, adverse selection

JEL Classification: C41, C61, G11