Limit Order Book Simulation and Trade Evaluation with $K$-Nearest-Neighbor Resampling

TL;DR

This paper introduces a $K$-nearest neighbor resampling method for simulating limit order book markets, enabling realistic trading strategy evaluation with theoretical guarantees and improved performance over deep learning approaches.

Contribution

The paper presents a novel $K$-NN resampling technique for LOB simulation that is easy to implement, computationally efficient, and outperforms existing deep learning methods in key statistics.

Findings

Realistic LOB dynamics can be simulated using the proposed method.

The method outperforms deep learning algorithms in benchmark tests.

Market impact in synthetic trading aligns with literature expectations.

Abstract

In this paper, we show how $K$-nearest neighbor ($K$-NN) resampling, an off-policy evaluation method proposed in \cite{giegrich2023k}, can be applied to simulate limit order book (LOB) markets and how it can be used to evaluate and calibrate trading strategies. Using historical LOB data, we demonstrate that our simulation method is capable of recreating realistic LOB dynamics and that synthetic trading within the simulation leads to a market impact in line with the corresponding literature. Compared to other statistical LOB simulation methods, our algorithm has theoretical convergence guarantees under general conditions, does not require optimization, is easy to implement and computationally efficient. Furthermore, we show that in a benchmark comparison our method outperforms a deep learning-based algorithm for several key statistics. In the context of a LOB with pro-rata type matching, we demonstrate how our algorithm can calibrate the size of limit orders for a liquidation strategy. Finally, we describe how $K$-NN resampling can be modified for choices of higher dimensional state spaces.