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.

Market making with minimum resting times

“…Also, note that the timescale of the MRT is seconds, so employing more realistic, yet mathematically more challenging, performance criteria will not add further insights. For example, we could assume that the performance criterion of the MM is expected utility of wealth or a mean-variance approach, both of which are employed in the extant literature by many authors, see Cheridito and Sepin (2014), Lorenz and Almgren (2011), Guéant (2015), Schied et al (2010), Donnelly and Gan (2018).…”

Optimal Liquidation in a Level-I Limit Order Book for Large-Tick Stocks

“…Cartea and Jaimungal [12] seek to execute a large order employing both market and limit orders, and solve the optimal strategies under different scenarios. Some researchers focus on the second layer and study how to optimally execute a single child order, for the purpose of incorporating information on the LOB market microstructure into their trading strategies, in particular Stoikov and Waeber [43], Donnellya and Gan [18] and Gonzalez and Schervish [22] for market-order-oriented, limit-order-oriented and hybrid optimal strategy, respectively. Finally, Cont and Kukanov [15] combine the last two layers together and propose a strategy that optimally distributes a child order across different order types and trading venues.…”