market microstructure modeling

This work addresses key limitations of Hawkes processes in market microstructure modeling—namely, instability, calibration difficulty, and irreproducible simulation. We propose a reproducible research framework integrating a deterministic C++ limit-order-book (LOB) simulator with a multivariate marked Hawkes process. Methodologically, we provide the first rigorous theoretical proofs of stability and ergodicity for both linear and nonlinear Hawkes models, revealing the critical role of the subcritical regime in capturing order-flow clustering. Calibration employs an exponential–power-law hybrid kernel, combined with time-rescaling and goodness-of-fit diagnostics for precision. Our framework successfully reproduces temporal clustering characteristics of real order flows on Binance BTC/USDT and LOBSTER AAPL datasets. All code, data, and configuration files are publicly released, enabling fully reproducible high-frequency market dynamics research.

Existing limit order book simulators struggle to accurately reproduce realistic execution costs, profit-and-loss outcomes, and microstructural dynamics. This work proposes an interactive simulator tailored for large-tick assets, which projects the order book state into a low-dimensional representation based on spread and volume imbalance, calibrates event timing to match the temporal structure of real markets, and incorporates a signed trade-flow feedback mechanism governed by a power-law decay kernel to capture market impact and its partial reversal. The proposed “project–estimate–validate–adapt” four-step framework is the first to simultaneously reproduce concave market impact, post-trade price reversion, and sensitivity to round-trip exchange latency within simulation. Experiments demonstrate that the approach generates highly realistic execution behavior across multiple stocks and trading strategies, significantly narrowing the gap between simulated and real-world market dynamics.

This study challenges the conventional view that liquidity, supply, and demand are fundamental economic variables, arguing instead that they emerge from the geometric structure induced by order book observations. By modeling the market as an expanding relational system devoid of predefined metrics, time, or price coordinates, and applying spectral embedding of the graph Laplacian to obtain a one-dimensional projection, the authors derive a price-like coordinate and a corresponding liquidity distribution. Remarkably, this approach reproduces canonical order book regularities without invoking assumptions about agent behavior. Using high-frequency Level II data from U.S. equities, the research demonstrates the cross-asset universality of a cumulative gamma-shaped liquidity profile, with information criteria confirming its superior fit compared to existing models.

This study systematically investigates the impact of relative tick size on limit order book (LOB) microstructure, aiming to identify and quantify distinct characteristics across assets with large, medium, and small tick sizes. We propose the first multidimensional Hawkes process model capable of smoothly capturing cross-tick-size LOB dynamics—unifying the modeling of order sparsity, multi-level price jumps, and bid-ask spread shape. We introduce the first formal microstructural criterion for classifying small-tick stocks. Furthermore, we uncover a universal mapping between tick size and order flow dynamics. The model is validated against empirical stylized facts, successfully reproducing key small-tick LOB features—including sparsity, spread shape, and heavy-tailed, leptokurtic return distributions—and enables continuous parameter-driven simulation of LOB evolution from large- to small-tick regimes, demonstrating its cross-asset generalizability.

This paper addresses the optimal execution problem under time- and size-constrained trading scenarios. Methodologically, it proposes a reinforcement learning (RL)-based autonomous decision-making framework that pioneers an end-to-end training paradigm integrating the ABIDES multi-agent market simulator with a customized Markov Decision Process (MDP) formulation. The framework dynamically learns execution policies directly from real-time limit-order-book (LOB) states, eliminating reliance on historical market data. It incorporates domain-informed LOB feature engineering and adapts both Proximal Policy Optimization (PPO) and Deep Q-Network (DQN) algorithms. Empirical evaluation demonstrates significant and robust improvements over benchmark strategies—including TWAP and VWAP—across key metrics: transaction cost (market impact), order completion rate, and timing risk. These results validate the efficacy and practicality of simulation-driven RL for algorithmic trade execution.

This study addresses the trade-off among execution probability, adverse selection, and opportunity cost in limit order trading by proposing a mesoscale optimal passive execution strategy. Embedding two empirically observed microstructural features—namely, the exponential decay of limit order fill probability with quote distance and the short-term linear price response to order flow imbalance—into a stochastic control framework, the work derives for the first time a passively induced market impact rate exhibiting exponential decay and solves for the corresponding optimal liquidation policy. The model is validated on both NASDAQ equity and foreign exchange data and extends naturally to settings involving heterogeneous decay rates, instantaneous impact, and target execution schedules, thereby establishing a theoretical foundation and practical mechanism for tactical passive execution.

This study proposes a unified explanation for several stylized facts in financial markets—namely, the persistence of order flow, the roughness of trading volume and volatility, and power-law market impact. By constructing a microstructural model that distinguishes between core and reactive order flows, both modeled as Hawkes processes governed by a single long-memory parameter \( H_0 \), the authors derive the joint asymptotic behavior of these quantities under a no-arbitrage constraint. Leveraging fractional stochastic calculus, rough path theory, and scaling limit analysis, they show that an empirically estimated \( H_0 \approx 3/4 \) not only reproduces the square-root market impact law but also aligns precisely with the observed roughness of volume and volatility. This work thus reveals, for the first time, a common underlying mechanism linking these phenomena through a single parsimonious parameter.

This study investigates stable cross-asset microstructural patterns in cryptocurrency limit order books and their predictive power for short-term returns. Leveraging second-level data from Binance Futures, the authors employ a unified CatBoost framework with a direction-aware GMADL objective function and time-series cross-validation to systematically analyze the stability of feature importance and SHAP dependence across multiple assets. Findings are interpreted through the lens of classical market microstructure theory. Notably, the paper empirically validates adverse selection theory by contrasting market-making and taker strategies during flash crash events, thereby uncovering systemic risks inherent in algorithmic trading. The research reveals highly consistent and transferable feature patterns across assets of varying market capitalizations—such as BTC and LTC—and demonstrates their practical trading viability through conservative order book backtesting.