The effect of latency on optimal order execution policy

Paper: arXiv 2504.00846

Authors: Chutian Ma, Giacinto Paolo Saggese, Paul Smith

Abstract

Market participants regularly send bid and ask quotes to exchange-operated limit order books. This creates an optimization challenge where their potential profit is determined by their quoted price and how often their orders are successfully executed. The expected profit from successful execution at a favorable limit price needs to be balanced against two key risks: (1) the possibility that orders will remain unfilled, which hinders the trading agenda and leads to greater price uncertainty, and (2) the danger that limit orders will be executed as market orders, particularly in the presence of order submission latency, which in turn results in higher transaction costs. In this paper, we consider a stochastic optimal control problem where a risk-averse trader attempts to maximize profit while balancing risk. The market is modeled using Brownian motion to represent the price uncertainty. We analyze the relationship between fill probability, limit price, and order submission latency. We derive closed-form approximations of these quantities that perform well in the practical regime of interest. Then, we utilize a mean-variance method where our total reward function features a risk-tolerance parameter to quantify the combined risk and profit.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 3.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper provides a rigorous mathematical treatment of latency in optimal order execution using stochastic control, hitting time distributions of Brownian motion, and dynamic programming. However, it relies heavily on analytical formulations and Monte Carlo simulations rather than empirical backtesting on real-world high-frequency limit order book data.

Research Flowchart

  flowchart TD
    A["Research Goal:<br>Optimize Limit Order Execution<br>under Latency & Risk"] --> B["Inputs:<br>Price Uncertainty (Brownian Motion)<br>& Latency Parameters"]
    B --> C["Stochastic Optimal Control<br>& Fill Probability Modeling"]
    C --> D["Derive Closed-Form<br>Approximations"]
    D --> E["Apply Mean-Variance Method<br>with Risk-Tolerance Parameter"]
    E --> F["Outcomes:<br>Balanced Profit/Risk Policy<br>& Latency Impact Analysis"]

Cited References (28)

1. Handbook of B rownian M otion – F acts and F ormulae (2015)
2. Trades, Q uotes and P rices (2018)
3. Algorithmic T rading (2020)
4. Econometric models of limit-order executions (2002) — link
5. Th 'e orie de la sp 'e culation (1900)
6. The P ricing of O ptions and C orporate L iabilities (1973)
7. Theory of R ational O ption P ricing (1973)
8. An I ntertemporal C apital A sset P ricing M odel (1973)

0 of 28 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.