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

Paper: arXiv 2409.06514

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.

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 8.0/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper utilizes advanced mathematical concepts from stochastic calculus and metric space theory for K-NN resampling with convergence proofs, while demonstrating rigorous empirical validation using historical LOB data, outperforming deep learning benchmarks and providing specific calibration examples for trading strategies.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Simulate LOB & Evaluate/Calibrate Trading<br>using K-NN Resampling"] --> B["Data & Inputs"]
  B --> C["Methodology: K-NN Resampling"]
  
  subgraph C ["Methodology: K-NN Resampling"]
      direction LR
      C1["Identify State Space"] --> C2["Find K-Nearest<br>Historical Neighbors"] --> C3["Resample Future<br>Transitions/Outcomes"]
  end

  C --> D["Computational Process"]
  
  subgraph D ["Computational Process"]
      direction LR
      D1["Market Simulation<br>Recreate LOB Dynamics"] --> D2["Strategy Evaluation<br>Simulate Synthetic Trading"]
  end

  D --> E["Key Findings & Outcomes"]
  
  subgraph E ["Key Findings & Outcomes"]
      E1["Validated Market Impact<br>Matches Literature"]
      E2["Outperformed Deep Learning<br>in Benchmark Stats"]
      E3["Calibrated Liquidation<br>Strategy Order Sizes"]
      E4["Extensible to<br>Higher Dimensional States"]
  end

Cited References (49)

1. Limit Order Book Simulation with Generative Adversarial Networks (2023)
2. Inferring term rates from SOFR futures prices (2019)
3. Three-Month SOFR (2024)
4. Generative AI for End-to-End Limit Order Book Modelling: A Token-Level Autoregressive Generative Model of Message Flow Using a Deep State Space Network (2023)
5. Combining parametric and nonparametric models for off-policy evaluation (2019)
6. Handbook of Price Impact Modeling (2023)
7. No-dynamic-arbitrage and market impact (2010)
8. Market impacts and the life cycle of investors orders (2015)

2 of 49 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.