Optimal Decisions in a Time Priority Queue

ABSTRACT

We show how the position of a limit order (LO) 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 LO book events and propose novel ways for modelling some of these events, including cancellation of LOs 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 LOs. 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 an 8.8% lower standard deviation for the same level of mean. This extra gain stems from posting an LO during adverse conditions and obtaining a good queue position before conditions become favourable.

KEYWORDS:

• Algorithmic trading
• high frequency trading
• limit order book
• queuing model
• impulse control
• adverse selection

Acknowledgements

The authors would like to thank Sebastian Jaimungal (University of Toronto) and Yaroslav Melnyk (EPFL) for their comments and suggestions, as well as participants at the Research in Options 2016 conference and the Conference on Mathematical Modelling in Finance 2017.

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

1. For each $\mathrm{\ell }$, we compute $f_{z,\mathrm{\ell }}=\frac{T_{z,\mathrm{\ell }}}{{\sum }_l{T}_{z,\mathrm{\ell }}}$, the fraction of time that the queue length is equal to $\mathrm{\ell }$ when the LOB is in regime $z$. The upper and lower truncation thresholds are defined as ${\bar{\mathrm{\ell }}}_z=min\left\{\mathrm{\ell }:{\sum }_{m\le \mathrm{\ell }}{f}_{z,m}\ge 0.01\right\}$ and ${\underset{\_}{\ell }}_z=\max \left\{\ell :{\displaystyle {\sum }_{m\le \ell }{f}_{z,m}}\le 0.99\right\}$.

2. The details given here show that the number of additions and cancellations are computed in a volume weighted fashion. Thus, even though we assume they have unit volume, the resulting intensities of the events will be larger to compensate for this discrepancy producing roughly equal expected volumes of added and cancelled orders.