Correlation emergence in two coupled simulated limit order books

ArXiv ID: 2408.03181 “View on arXiv”

Authors: Unknown

Abstract

We use random walks to simulate the fluid limit of two coupled diffusive limit order books to model correlation emergence. The model implements the arrival, cancellation and diffusion of orders coupled by a pairs trader profiting from the mean-reversion between the two order books in the fluid limit for a Lit order book with vanishing boundary conditions and order volume conservation. We are able to demonstrate the recovery of an Epps effect from this. We discuss how various stylised facts depend on the model parameters and the numerical scheme and discuss the various strengths and weaknesses of the approach. We demonstrate how the Epps effect depends on different choices of time and price discretisation. This shows how an Epps effect can emerge without recourse to market microstructure noise relative to a latent model but can rather be viewed as an emergent property arising from trader interactions in a world of asynchronous events.

Keywords: Random Walks, Limit Order Books, Epps Effect, Pairs Trading, Market Microstructure, Equities

Complexity vs Empirical Score

• Math Complexity: 8.0/10
• Empirical Rigor: 3.0/10
• Quadrant: Lab Rats
• Why: The paper presents a sophisticated coupled reaction-diffusion PDE model with fractional calculus, requiring advanced mathematics to derive and solve, but it is a theoretical simulation study that lacks real-world backtesting, live data, or implementation-heavy validation.

  flowchart TD
    A["Research Goal: Model correlation emergence in coupled limit order books"] --> B["Methodology: Random Walks for Diffusive Limit Order Books"]
    B --> C["Data/Inputs: Arrival, Cancellation & Diffusion of Orders"]
    C --> D["Computational Process: Pairs Trader Coupling & Vanishing Boundary Conditions"]
    D --> E["Key Findings: Recovery of Epps Effect & Emergent Correlation"]