How Trader Interactions Create Correlation and the Epps Effect

Summary

This study uses random walks to simulate two coupled limit order books and examine how correlation develops between them. Its model represents order arrivals, cancellations, and diffusion, while a pairs trader links the books by trading on mean reversion. It conserves order volume and uses vanishing boundary conditions in a fluid limit. The simulations recover an Epps effect: measured correlation changes with the time scale of observation, and the study examines how that pattern responds to time and price discretisation.

The results suggest that an Epps effect can emerge from asynchronous events and trader interaction, without adding market microstructure noise relative to a latent-price model. The authors also discuss how model parameters and the numerical scheme affect stylised facts, and identify strengths and weaknesses of the approach. The evidence is simulation-based, so it shows a mechanism that can generate the effect rather than establishing that this is its cause in real markets.

Key ideas

• Coupling two simulated order books through a mean-reversion pairs trader can produce correlation between them.
• The model represents order arrivals, cancellations, and diffusion while conserving order volume.
• The simulations recover an Epps effect whose appearance depends on time and price discretisation.
• Asynchronous trader interactions offer a possible source of the effect without latent-price microstructure noise.
• The findings depend on model parameters and numerical choices, so they do not establish the mechanism in real markets.

Tags

# Correlation emergence in two coupled simulated limit order books


# Correlation emergence in two coupled simulated limit order books









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.