A Novel Approach to Queue-Reactive Models: The Importance of Order Sizes

Abstract: In this article, we delve into the applications and extensions of the queue-reactive model for the simulation of limit order books. Our approach emphasizes the importance of order sizes, in conjunction with their type and arrival rate, by integrating the current state of the order book to determine, not only the intensity of order arrivals and their type, but also their sizes. These extensions generate simulated markets that are in line with numerous stylized facts of the market. Our empirical calibration, using futures on German bonds, reveals that the extended queue-reactive model significantly improves the description of order flow properties and the shape of queue distributions. Moreover, our findings demonstrate that the extended model produces simulated markets with a volatility comparable to historical real data, utilizing only endogenous information from the limit order book. This research underscores the potential of the queue-reactive model and its extensions in accurately simulating market dynamics and providing valuable insights into the complex nature of limit order book modeling.

• The paper shows that integrating order sizes into queue-reactive models significantly improves LOB simulation accuracy.
• It introduces FTQR and SAQR extensions to capture complete queue events and order size effects with calibrated Bund futures data.
• Empirical evaluations reveal that the SAQR model better reproduces market dynamics and queue size distributions compared to Hawkes processes.

Summary of "A Novel Approach to Queue-Reactive Models: The Importance of Order Sizes"

Introduction

The paper presents an extension of the queue-reactive model designed for accurate limit order book (LOB) simulations, emphasizing the inclusion of order sizes in conjunction with order types and arrival rates. Through empirical studies utilizing German bond futures, the authors demonstrate that incorporating order sizes markedly enhances the model’s ability to reflect real market dynamics, offering valuable insights into LOB microstructure modeling.

Methodology

Queue-Reactive Model

The Queue-Reactive (QR) model serves as a foundational framework, using order arrival intensities as a function of queue sizes and types—limit, cancel, and market orders. The core advantage of QR lies in its ability to reflect multiple stylized facts through behavior analyses of queue size evolution over time and price change dynamics. By calibrating event intensities with Bund futures data, the model captures the heterogeneity of market participant strategies and their implications on queue priorities.

Figure 1: Illustration of queue size evolution. This diagram represents the sequential updates in the size of a given queue over time. Initially, the queue size is $q_{k-1}$.

Extensions: FTQR and SAQR

Two key extensions are introduced to address the limitations of the QR model, notably its inability to mirror historical volatility due to slower LOB progression:

1. Five-Type Queue-Reactive Model (FTQR): Incorporates complete queue consumption events (market_all and cancel_all). This adjustment accounts for scenarios where participants consume entire queue sizes, calibrated to reflect high excitement during scarce liquidity.

   Figure 2: Results of queue-reactive model on Bund futures - Intensities as functions of queue size (best levels).

2. Size-Aware Queue-Reactive Model (SAQR): Models order size impact, where the intensity is a function of both order type and size. This adaptation improves the realism of order size distribution, especially when queue sizes are small or orders consume entire liquidity.

   Figure 3: Matrix heatmap of normalized calibrated intensities On Bund future data (logarithmic scale).

Results

The empirical evaluation of the model variants against key market stylized facts—including price dynamics, volatility, traded volume, and order book distribution—highlights the superior alignment of the SAQR model with actual market behaviors. The SAQR model demonstrates an improved fit for the Gamma distribution of queue sizes and realistic signature plots showcasing volatility at different scales.

Figure 4: Distribution of order book volumes and Gamma law fit.

Hawkes Process Integration

In comparison, models employing Hawkes processes effectively reflect excitation dynamics between events but show discrepancies in reproducing queue size distributions. The analysis suggests that although Hawkes processes capture clustering effects and contagion phenomena, their integration with queue-reactive frameworks necessitates adjustments to reconcile ergodicity issues inherent in Poisson-based approaches.

Conclusion

The study underscores the significance of incorporating order sizes into queue-reactive models, substantially enhancing their ability to simulate authentic market microstructure dynamics. Future research directions include integrating more complex excitation dynamics and addressing intra-day seasonality, motivated by the nuanced performance of the SAQR model in aligning with observed market behaviors. The insights gleaned from these methodological advancements serve pivotal roles in refining trading strategies and improving market risk management processes.