The Impact of Execution Latency on Optimal High-Frequency Market Making

Abstract

High-Frequency Trading strategies rely on low-latency execution to maintain profitability when competing against other firms. This project will study the quantitative impacts of bid-ask order execution latency while under stochastic price dynamics. I will build upon the predefined Avellaneda–Stoikov model by adding a static execution delay within the control process, modelling latency as the time between quote submission and order execution.

A simulation engine will be implemented to evaluate profitability, inventory variance, and risk-adjusted returns across a range of latency regimes. Empirical order book data will be used to validate the model’s assumptions and order intensities for calibration.

Axioms

The following statements will be taken as axioms for this project for the benefit of simplicity and the removal of any potential boundary cases:

  • The mid-price will follow a diffusion process.
  • Order arrivals are modelled as Poisson processes.
  • Order intensity is dependent on quote distance.

1. Introduction

All electronic financial markets operate through limit order books (LOBs), where liquidity providers post buy and sell limit orders, and liquidity takers execute orders against them. High-frequency market makers seek profitability in the bid-ask spread while managing inventory risk.

Latency

The delay between signal generation, order submission, and execution plays an important role in determining competitive advantage. Thus, when latency is non-zero, bid and ask prices may inaccurately reflect current market conditions, increasing adverse selection risk.

This paper will address the following question:

How does fixed execution latency alter the optimal strategy and profitability of a stochastic market maker?

I will extend the Avellaneda Stoikov 2005 optimal control process by introducing a deterministic latency parameter to derive the optimal spreads. The theoretical results are tested in a Monte Carlo simulation and validated against empirical order book statistics.