transaction-level price-formation 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.

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 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.

Automated Market Makers (AMMs) in DeFi face adverse selection in blue-chip asset pairs: arbitrage—while essential for revenue—is also a primary source of losses due to “informed order flow.” Method: We develop a differential-equation-based arbitrage dynamics model, integrating sensitivity analysis and numerical simulation to systematically quantify how fee structures affect arbitrage behavior, uninformed trading incentives, and net revenue. Contribution/Results: We propose a directional dynamic fee mechanism—where fees adjust asymmetrically with price movement direction—to suppress toxic flow while preserving benign liquidity. Our analysis reveals that the optimal static fee lies within a narrow range; in contrast, the dynamic mechanism increases AMM net revenue by 18–32% empirically and reduces adverse selection losses by over 40%. This work provides a theoretically grounded, empirically testable framework for AMM fee design.

In decentralized finance (DeFi), arbitrage against blue-chip asset pairs in automated market makers (AMMs) constitutes a primary revenue source but also induces substantial impermanent loss (IL) due to informed order flow. The central challenge lies in suppressing informed arbitrage while preserving liquidity for uninformed trades. Method: This paper introduces the first analytical model of AMM arbitrage dynamics as a stochastic walk with state-dependent rewards, yielding a tractable theoretical framework for fee optimization. Through rigorous stochastic process analysis, sensitivity analysis, and quantification of value retention, we derive closed-form relationships between fee rates and pool asset value preservation. Results: We formally prove the existence of an optimal fee rate and characterize its structural properties—balancing revenue generation against IL mitigation. This work establishes the first analytically rigorous and practically actionable paradigm for designing AMM fee mechanisms.

This study addresses the limitation of traditional limit order book models in neglecting the geometric essence of market microstructure. The authors propose a relational pre-geometric framework that eschews predefined metrics, time, or price coordinates. By applying degree reduction and low-dimensional spectral projection to the transactional interaction structure, price-like coordinates and liquidity density emerge naturally, revealing the complementarity between bid and ask sides. A key innovation lies in decomposing liquidity imbalance into rigid drift and geometric shear modes—the latter reshapes order book structure without inducing price changes and yields a gamma-like liquidity distribution under shear constraints. Empirical validation using high-frequency Level II data from U.S. equities demonstrates that the model significantly outperforms conventional cumulative models in both goodness-of-fit and residual diagnostics.

This study addresses the decomposition of permanent price movements from transient microstructure noise using tick-by-tick transaction data and provides a microstructural foundation for rough noise observed at macroscopic scales. To this end, the authors develop a structural microstructure model that explicitly distinguishes between these two components and demonstrate its weak convergence to a semimartingale with a rough noise term in the macroscopic limit. This work establishes, for the first time, a microfounded theoretical basis for rough noise models grounded in high-frequency data, revealing their non-universality and pronounced intraday variability. Employing generalized method of moments (GMM) estimation coupled with formal statistical tests—validated through simulations to perform well in finite samples—the empirical analysis of 2024 Dow Jones constituents shows that rough noise is statistically significant only on days dominated by short-term price reversals, with estimated roughness exponents typically near zero.

This study addresses the reproducibility challenges of the multi-market fragmentation and delayed arbitrage agent-based model proposed by Wah and Wellman (2016), which stemmed from insufficient implementation details and limited quantitative reporting. Leveraging the authors’ subsequently released code, we formalize the modeling process using the ODD protocol and enhance statistical robustness by increasing simulation runs and applying bootstrapping to construct confidence intervals. Our replication achieves relational equivalence across most metrics but rejects quantitative alignment under non-zero delay conditions. Notably, we uncover that conclusions regarding fragmentation effects are highly sensitive to the specific implementation of greedy strategies; under alternative strategies, market fragmentation actually reduces execution time and improves trader welfare. This work thus provides the first complete and transparent replication framework for the original model.

This study addresses a central challenge in financial market microstructure: validating the order-splitting theory’s explanation of long-range correlations in market order flow without access to trader identity information. Leveraging three years of public TAQ data from the Johannesburg Stock Exchange, the authors propose a novel synthetic meta-order reconstruction method that relies solely on publicly available data. Under plausible assumptions of either 50 or 150 effective traders, the approach successfully replicates the autocorrelation structure of order flow predicted by the Lillo-Mike-Farmer (LMF) model. This work provides the first empirical validation of the LMF theory in the absence of trader-identified data, thereby overcoming the field’s traditional reliance on proprietary datasets and significantly enhancing the reproducibility and cross-market applicability of empirical findings.

This study addresses the lack of a systematic understanding of market efficiency and return structures in automated market makers (AMMs) under the dynamic interaction between liquidity providers (LPs) and arbitrageurs. The authors develop a dynamic equilibrium framework for constant function market makers (CFMMs) that integrates slippage, trading fees, price impact, noise trading, endogenous gas fees, and time-varying volatility to capture strategic interactions among heterogeneous participants. They uncover an inherent bid–ask asymmetry in CFMMs, demonstrate that liquidity provision is strictly dominated in a pure arbitrage environment, and establish a non-degenerate interior equilibrium incorporating execution costs, which explains the inverted-U relationship between liquidity supply and volatility. Combining dynamic game-theoretic modeling, closed-form solutions, and on-chain data calibration, the paper empirically validates asymmetric price impact and non-monotonic optimal liquidity provision, offering theoretical foundations for AMM mechanism design and LP strategies.