High-Frequency Trading

Intraday Limit Order Price Change Transition Dynamics Across Market Capitalizations Through Markov Analysis ArXiv ID: 2601.04959 “View on arXiv” Authors: Salam Rabindrajit Luwang, Kundan Mukhia, Buddha Nath Sharma, Md. Nurujjaman, Anish Rai, Filippo Petroni Abstract Quantitative understanding of stochastic dynamics in limit order price changes is essential for execution strategy design. We analyze intraday transition dynamics of ask and bid orders across market capitalization tiers using high-frequency NASDAQ100 tick data. Employing a discrete-time Markov chain framework, we categorize consecutive price changes into nine states and estimate transition probability matrices (TPMs) for six intraday intervals across High ($\mathtt{“HMC”}$), Medium ($\mathtt{“MMC”}$), and Low ($\mathtt{“LMC”}$) market cap stocks. Element-wise TPM comparison reveals systematic patterns: price inertia peaks during opening and closing hours, stabilizing midday. A capitalization gradient is observed: $\mathtt{“HMC”}$ stocks exhibit the strongest inertia, while $\mathtt{“LMC”}$ stocks show lower stability and wider spreads. Markov metrics, including spectral gap, entropy rate, and mean recurrence times, quantify these dynamics. Clustering analysis identifies three distinct temporal phases on the bid side – Opening, Midday, and Closing, and four phases on the ask side by distinguishing Opening, Midday, Pre-Close, and Close. This indicates that sellers initiate end-of-day positioning earlier than buyers. Stationary distributions show limit order dynamics are dominated by neutral and mild price changes. Jensen-Shannon divergence confirms the closing hour as the most distinct phase, with capitalization modulating temporal contrasts and bid-ask asymmetry. These findings support capitalization-aware and time-adaptive execution algorithms. ...

Temporal Kolmogorov-Arnold Networks (T-KAN) for High-Frequency Limit Order Book Forecasting: Efficiency, Interpretability, and Alpha Decay ArXiv ID: 2601.02310 “View on arXiv” Authors: Ahmad Makinde Abstract High-Frequency trading (HFT) environments are characterised by large volumes of limit order book (LOB) data, which is notoriously noisy and non-linear. Alpha decay represents a significant challenge, with traditional models such as DeepLOB losing predictive power as the time horizon (k) increases. In this paper, using data from the FI-2010 dataset, we introduce Temporal Kolmogorov-Arnold Networks (T-KAN) to replace the fixed, linear weights of standard LSTMs with learnable B-spline activation functions. This allows the model to learn the ‘shape’ of market signals as opposed to just their magnitude. This resulted in a 19.1% relative improvement in the F1-score at the k = 100 horizon. The efficacy of T-KAN networks cannot be understated, producing a 132.48% return compared to the -82.76% DeepLOB drawdown under 1.0 bps transaction costs. In addition to this, the T-KAN model proves quite interpretable, with the ‘dead-zones’ being clearly visible in the splines. The T-KAN architecture is also uniquely optimized for low-latency FPGA implementation via High level Synthesis (HLS). The code for the experiments in this project can be found at https://github.com/AhmadMak/Temporal-Kolmogorov-Arnold-Networks-T-KAN-for-High-Frequency-Limit-Order-Book-Forecasting. ...

Impact of Volatility on Time-Based Transaction Ordering Policies ArXiv ID: 2512.23386 “View on arXiv” Authors: Sunghun Ko, Jinsuk Park Abstract We study Arbitrum’s Express Lane Auction (ELA), an ahead-of-time second-price auction that grants the winner an exclusive latency advantage for one minute. Building on a single-round model with risk-averse bidders, we propose a hypothesis that the value of priority access is discounted relative to risk-neutral valuation due to the difficulty of forecasting short-horizon volatility and bidders’ risk aversion. We test these predictions using ELA bid records matched to high-frequency ETH prices and find that the result is consistent with the model. ...

High-Frequency Analysis of a Trading Game with Transient Price Impact ArXiv ID: 2512.11765 “View on arXiv” Authors: Marcel Nutz, Alessandro Prosperi Abstract We study the high-frequency limit of an $n$-trader optimal execution game in discrete time. Traders face transient price impact of Obizhaeva–Wang type in addition to quadratic instantaneous trading costs $θ(ΔX_t)^2$ on each transaction $ΔX_t$. There is a unique Nash equilibrium in which traders choose liquidation strategies minimizing expected execution costs. In the high-frequency limit where the grid of trading dates converges to the continuous interval $[“0,T”]$, the discrete equilibrium inventories converge at rate $1/N$ to the continuous-time equilibrium of an Obizhaeva–Wang model with additional quadratic costs $\vartheta_0(ΔX_0)^2$ and $\vartheta_T(ΔX_T)^2$ on initial and terminal block trades, where $\vartheta_0=(n-1)/2$ and $\vartheta_T=1/2$. The latter model was introduced by Campbell and Nutz as the limit of continuous-time equilibria with vanishing instantaneous costs. Our results extend and refine previous results of Schied, Strehle, and Zhang for the particular case $n=2$ where $\vartheta_0=\vartheta_T=1/2$. In particular, we show how the coefficients $\vartheta_0=(n-1)/2$ and $\vartheta_T=1/2$ arise endogenously in the high-frequency limit: the initial and terminal block costs of the continuous-time model are identified as the limits of the cumulative discrete instantaneous costs incurred over small neighborhoods of $0$ and $T$, respectively, and these limits are independent of $θ>0$. By contrast, when $θ=0$ the discrete-time equilibrium strategies and costs exhibit persistent oscillations and admit no high-frequency limit, mirroring the non-existence of continuous-time equilibria without boundary block costs. Our results show that two different types of trading frictions – a fine time discretization and small instantaneous costs in continuous time – have similar regularizing effects and select a canonical model in the limit. ...

Push-response anomalies in high-frequency S&P 500 price series ArXiv ID: 2511.06177 “View on arXiv” Authors: Dmitrii Vlasiuk, Mikhail Smirnov Abstract We test the hypothesis that consecutive intraday price changes in the most liquid U.S. equity ETF (SPY) are conditionally nonrandom. Using NBBO event-time data for about 1,500 regular trading days, we form for every lag L ordered pairs of a backward price increment (“push”) and a forward price increment (“response”), standardize them, and estimate the expected responses on a fine grid of push magnitudes. The resulting lag-by-magnitude maps reveal a persistent structural shift: for short lags (1-5,000 ticks), expected responses cluster near zero across most push magnitudes, suggesting high short-term efficiency; beyond that range, pronounced tails emerge, indicating that larger historical pushes increasingly correlate with nonzero conditional responses. We also find that large negative pushes are followed by stronger positive responses than equally large positive pushes, consistent with asymmetric liquidity replenishment after sell-side shocks. Decomposition into symmetric and antisymmetric components and the associated dominance curves confirm that short-horizon efficiency is restored only partially. The evidence points to an intraday, lag-resolved anomaly that is invisible in unconditional returns and that can be used to define tradable pockets and risk controls. ...

JaxMARL-HFT: GPU-Accelerated Large-Scale Multi-Agent Reinforcement Learning for High-Frequency Trading ArXiv ID: 2511.02136 “View on arXiv” Authors: Valentin Mohl, Sascha Frey, Reuben Leyland, Kang Li, George Nigmatulin, Mihai Cucuringu, Stefan Zohren, Jakob Foerster, Anisoara Calinescu Abstract Agent-based modelling (ABM) approaches for high-frequency financial markets are difficult to calibrate and validate, partly due to the large parameter space created by defining fixed agent policies. Multi-agent reinforcement learning (MARL) enables more realistic agent behaviour and reduces the number of free parameters, but the heavy computational cost has so far limited research efforts. To address this, we introduce JaxMARL-HFT (JAX-based Multi-Agent Reinforcement Learning for High-Frequency Trading), the first GPU-accelerated open-source multi-agent reinforcement learning environment for high-frequency trading (HFT) on market-by-order (MBO) data. Extending the JaxMARL framework and building on the JAX-LOB implementation, JaxMARL-HFT is designed to handle a heterogeneous set of agents, enabling diverse observation/action spaces and reward functions. It is designed flexibly, so it can also be used for single-agent RL, or extended to act as an ABM with fixed-policy agents. Leveraging JAX enables up to a 240x reduction in end-to-end training time, compared with state-of-the-art reference implementations on the same hardware. This significant speed-up makes it feasible to exploit the large, granular datasets available in high-frequency trading, and to perform the extensive hyperparameter sweeps required for robust and efficient MARL research in trading. We demonstrate the use of JaxMARL-HFT with independent Proximal Policy Optimization (IPPO) for a two-player environment, with an order execution and a market making agent, using one year of LOB data (400 million orders), and show that these agents learn to outperform standard benchmarks. The code for the JaxMARL-HFT framework is available on GitHub. ...

When AI Trading Agents Compete: Adverse Selection of Meta-Orders by Reinforcement Learning-Based Market Making ArXiv ID: 2510.27334 “View on arXiv” Authors: Ali Raza Jafree, Konark Jain, Nick Firoozye Abstract We investigate the mechanisms by which medium-frequency trading agents are adversely selected by opportunistic high-frequency traders. We use reinforcement learning (RL) within a Hawkes Limit Order Book (LOB) model in order to replicate the behaviours of high-frequency market makers. In contrast to the classical models with exogenous price impact assumptions, the Hawkes model accounts for endogenous price impact and other key properties of the market (Jain et al. 2024a). Given the real-world impracticalities of the market maker updating strategies for every event in the LOB, we formulate the high-frequency market making agent via an impulse control reinforcement learning framework (Jain et al. 2025). The RL used in the simulation utilises Proximal Policy Optimisation (PPO) and self-imitation learning. To replicate the adverse selection phenomenon, we test the RL agent trading against a medium frequency trader (MFT) executing a meta-order and demonstrate that, with training against the MFT meta-order execution agent, the RL market making agent learns to capitalise on the price drift induced by the meta-order. Recent empirical studies have shown that medium-frequency traders are increasingly subject to adverse selection by high-frequency trading agents. As high-frequency trading continues to proliferate across financial markets, the slippage costs incurred by medium-frequency traders are likely to increase over time. However, we do not observe that increased profits for the market making RL agent necessarily cause significantly increased slippages for the MFT agent. ...

On Bellman equation in the limit order optimization problem for high-frequency trading ArXiv ID: 2510.15988 “View on arXiv” Authors: M. I. Balakaeva, A. Yu. Veretennikov Abstract An approximation method for construction of optimal strategies in the bid & ask limit order book in the high-frequency trading (HFT) is studied. The basis is the article by M. Avellaneda & S. Stoikov 2008, in which certain seemingly serious gaps have been found; in the present paper they are carefully corrected. However, a bit surprisingly, our corrections do not change the main answer in the cited paper, so that, in fact, the gaps turn out to be unimportant. An explanation of this effect is offered. ...

A Deterministic Limit Order Book Simulator with Hawkes-Driven Order Flow ArXiv ID: 2510.08085 “View on arXiv” Authors: Sohaib El Karmi Abstract We present a reproducible research framework for market microstructure combining a deterministic C++ limit order book (LOB) simulator with stochastic order flow generated by multivariate marked Hawkes processes. The paper derives full stability and ergodicity proofs for both linear and nonlinear Hawkes models, implements time-rescaling and goodness-of-fit diagnostics, and calibrates exponential and power-law kernels on Binance BTCUSDT and LOBSTER AAPL datasets. Empirical results highlight the nearly-unstable subcritical regime as essential for reproducing realistic clustering in order flow. All code, datasets, and configuration files are publicly available at https://github.com/sohaibelkarmi/High-Frequency-Trading-Simulator ...

Forecasting Liquidity Withdraw with Machine Learning Models ArXiv ID: 2509.22985 “View on arXiv” Authors: Haochuan, Wang Abstract Liquidity withdrawal is a critical indicator of market fragility. In this project, I test a framework for forecasting liquidity withdrawal at the individual-stock level, ranging from less liquid stocks to highly liquid large-cap tickers, and evaluate the relative performance of competing model classes in predicting short-horizon order book stress. We introduce the Liquidity Withdrawal Index (LWI) – defined as the ratio of order cancellations to the sum of standing depth and new additions at the best quotes – as a bounded, interpretable measure of transient liquidity removal. Using Nasdaq market-by-order (MBO) data, we compare a spectrum of approaches: linear benchmarks (AR, HAR), and non-linear tree ensembles (XGBoost), across horizons ranging from 250,ms to 5,s. Beyond predictive accuracy, our results provide insights into order placement and cancellation dynamics, identify regimes where linear versus non-linear signals dominate, and highlight how early-warning indicators of liquidity withdrawal can inform both market surveillance and execution. ...