Limit Order Book

Maximizing Battery Storage Profits via High-Frequency Intraday Trading ArXiv ID: 2504.06932 “View on arXiv” Authors: Unknown Abstract Maximizing revenue for grid-scale battery energy storage systems in continuous intraday electricity markets requires strategies that are able to seize trading opportunities as soon as new information arrives. This paper introduces and evaluates an automated high-frequency trading strategy for battery energy storage systems trading on the intraday market for power while explicitly considering the dynamics of the limit order book, market rules, and technical parameters. The standard rolling intrinsic strategy is adapted for continuous intraday electricity markets and solved using a dynamic programming approximation that is two to three orders of magnitude faster than an exact mixed-integer linear programming solution. A detailed backtest over a full year of German order book data demonstrates that the proposed dynamic programming formulation does not reduce trading profits and enables the policy to react to every relevant order book update, enabling realistic rapid backtesting. Our results show the significant revenue potential of high-frequency trading: our policy earns 58% more than when re-optimizing only once every hour and 14% more than when re-optimizing once per minute, highlighting that profits critically depend on trading speed. Furthermore, we leverage the speed of our algorithm to train a parametric extension of the rolling intrinsic, increasing yearly revenue by 8.4% out of sample. ...

Modeling metaorder impact with a Non-Markovian Zero Intelligence model ArXiv ID: 2503.05254 “View on arXiv” Authors: Unknown Abstract Devising models of the limit order book that realistically reproduce the market response to exogenous trades is extremely challenging and fundamental in order to test trading strategies. We propose a novel explainable model for small tick assets, the Non-Markovian Zero Intelligence, which is a variant of the well-known Zero Intelligence model. The main modification is that the probability of limit orders’ signs (buy/sell) is not constant but is a function of the exponentially weighted mid-price return, representing the past price dynamics, and can be interpreted as the reaction of traders with reservation prices to the price trend. With numerical simulations and analytical arguments, we show that the model predicts a concave price path during a metaorder execution and to a price reversion after the execution ends, as empirically observed. We analyze in-depth the mechanism at the root of the arising concavity, the components which constitute the price impact in our model, and the dependence of the results on the two main parameters, namely the time scale and the strength of the reaction of traders to the price trend. ...

TRADES: Generating Realistic Market Simulations with Diffusion Models ArXiv ID: 2502.07071 “View on arXiv” Authors: Unknown Abstract Financial markets are complex systems characterized by high statistical noise, nonlinearity, volatility, and constant evolution. Thus, modeling them is extremely hard. Here, we address the task of generating realistic and responsive Limit Order Book (LOB) market simulations, which are fundamental for calibrating and testing trading strategies, performing market impact experiments, and generating synthetic market data. We propose a novel TRAnsformer-based Denoising Diffusion Probabilistic Engine for LOB Simulations (TRADES). TRADES generates realistic order flows as time series conditioned on the state of the market, leveraging a transformer-based architecture that captures the temporal and spatial characteristics of high-frequency market data. There is a notable absence of quantitative metrics for evaluating generative market simulation models in the literature. To tackle this problem, we adapt the predictive score, a metric measured as an MAE, to market data by training a stock price predictive model on synthetic data and testing it on real data. We compare TRADES with previous works on two stocks, reporting a 3.27 and 3.48 improvement over SoTA according to the predictive score, demonstrating that we generate useful synthetic market data for financial downstream tasks. Furthermore, we assess TRADES’s market simulation realism and responsiveness, showing that it effectively learns the conditional data distribution and successfully reacts to an experimental agent, giving sprout to possible calibrations and evaluations of trading strategies and market impact experiments. To perform the experiments, we developed DeepMarket, the first open-source Python framework for LOB market simulation with deep learning. In our repository, we include a synthetic LOB dataset composed of TRADES’s generated simulations. ...

Agent-Based Simulation of a Perpetual Futures Market ArXiv ID: 2501.09404 “View on arXiv” Authors: Unknown Abstract I introduce an agent-based model of a Perpetual Futures market with heterogeneous agents trading via a central limit order book. Perpetual Futures (henceforth Perps) are financial derivatives introduced by the economist Robert Shiller, designed to peg their price to that of the underlying Spot market. This paper extends the limit order book model of Chiarella et al. (2002) by taking their agent and orderbook parameters, designed for a simple stock exchange, and applying it to the more complex environment of a Perp market with long and short traders who exhibit both positional and basis-trading behaviors. I find that despite the simplicity of the agent behavior, the simulation is able to reproduce the most salient feature of a Perp market, the pegging of the Perp price to the underlying Spot price. In contrast to fundamental simulations of stock markets which aim to reproduce empirically observed stylized facts such as the leptokurtosis and heteroscedasticity of returns, volatility clustering and others, in derivatives markets many of these features are provided exogenously by the underlying Spot price signal. This is especially true of Perps since the derivative is designed to mimic the price of the Spot market. Therefore, this paper will focus exclusively on analyzing how market and agent parameters such as order lifetime, trading horizon and spread affect the premiums at which Perps trade with respect to the underlying Spot market. I show that this simulation provides a simple and robust environment for exploring the dynamics of Perpetual Futures markets and their microstructure in this regard. Lastly, I explore the ability of the model to reproduce the effects of biasing long traders to trade positionally and short traders to basis-trade, which was the original intention behind the market design, and is a tendency observed empirically in real Perp markets. ...

Deep Learning Meets Queue-Reactive: A Framework for Realistic Limit Order Book Simulation ArXiv ID: 2501.08822 “View on arXiv” Authors: Unknown Abstract The Queue-Reactive model introduced by Huang et al. (2015) has become a standard tool for limit order book modeling, widely adopted by both researchers and practitioners for its simplicity and effectiveness. We present the Multidimensional Deep Queue-Reactive (MDQR) model, which extends this framework in three ways: it relaxes the assumption of queue independence, enriches the state space with market features, and models the distribution of order sizes. Through a neural network architecture, the model learns complex dependencies between different price levels and adapts to varying market conditions, while preserving the interpretable point-process foundation of the original framework. Using data from the Bund futures market, we show that MDQR captures key market properties including the square-root law of market impact, cross-queue correlations, and realistic order size patterns. The model demonstrates particular strength in reproducing both conditional and stationary distributions of order sizes, as well as various stylized facts of market microstructure. The model achieves this while maintaining the computational efficiency needed for practical applications such as strategy development through reinforcement learning or realistic backtesting. ...

Optimal Execution Strategies Incorporating Internal Liquidity Through Market Making ArXiv ID: 2501.07581 “View on arXiv” Authors: Unknown Abstract This paper introduces a new algorithmic execution model that integrates interbank limit and market orders with internal liquidity generated through market making. Based on the Cartea et al.\cite{“cartea2015algorithmic”} framework, we incorporate market impact in interbank orders while excluding it for internal market-making transactions. Our model aims to optimize the balance between interbank and internal liquidity, reducing market impact and improving execution efficiency. ...

Minimal Batch Adaptive Learning Policy Engine for Real-Time Mid-Price Forecasting in High-Frequency Trading ArXiv ID: 2412.19372 “View on arXiv” Authors: Unknown Abstract High-frequency trading (HFT) has transformed modern financial markets, making reliable short-term price forecasting models essential. In this study, we present a novel approach to mid-price forecasting using Level 1 limit order book (LOB) data from NASDAQ, focusing on 100 U.S. stocks from the S&P 500 index during the period from September to November 2022. Expanding on our previous work with Radial Basis Function Neural Networks (RBFNN), which leveraged automated feature importance techniques based on mean decrease impurity (MDI) and gradient descent (GD), we introduce the Adaptive Learning Policy Engine (ALPE) - a reinforcement learning (RL)-based agent designed for batch-free, immediate mid-price forecasting. ALPE incorporates adaptive epsilon decay to dynamically balance exploration and exploitation, outperforming a diverse range of highly effective machine learning (ML) and deep learning (DL) models in forecasting performance. ...

A theory of passive market impact ArXiv ID: 2412.07461 “View on arXiv” Authors: Unknown Abstract While the market impact of aggressive orders has been extensively studied, the impact of passive orders, those executed through limit orders, remains less understood. The goal of this paper is to investigate passive market impact by developing a microstructure model connecting liquidity dynamics and price moves. A key innovation of our approach is to replace the traditional assumption of constant information content for each trade by a function that depends on the available volume in the limit order book. Within this framework, we explore scaling limits and analyze the market impact of passive metaorders. Additionally, we derive useful approximations for the shape of market impact curves, leading to closed-form formulas that can be easily applied in practice. ...

Reinforcement Learning in Non-Markov Market-Making ArXiv ID: 2410.14504 “View on arXiv” Authors: Unknown Abstract We develop a deep reinforcement learning (RL) framework for an optimal market-making (MM) trading problem, specifically focusing on price processes with semi-Markov and Hawkes Jump-Diffusion dynamics. We begin by discussing the basics of RL and the deep RL framework used, where we deployed the state-of-the-art Soft Actor-Critic (SAC) algorithm for the deep learning part. The SAC algorithm is an off-policy entropy maximization algorithm more suitable for tackling complex, high-dimensional problems with continuous state and action spaces like in optimal market-making (MM). We introduce the optimal MM problem considered, where we detail all the deterministic and stochastic processes that go into setting up an environment for simulating this strategy. Here we also give an in-depth overview of the jump-diffusion pricing dynamics used, our method for dealing with adverse selection within the limit order book, and we highlight the working parts of our optimization problem. Next, we discuss training and testing results, where we give visuals of how important deterministic and stochastic processes such as the bid/ask, trade executions, inventory, and the reward function evolved. We include a discussion on the limitations of these results, which are important points to note for most diffusion models in this setting. ...

No Tick-Size Too Small: A General Method for Modelling Small Tick Limit Order Books ArXiv ID: 2410.08744 “View on arXiv” Authors: Unknown Abstract Tick-sizes not only influence the granularity of the price formation process but also affect market agents’ behavior. We investigate the disparity in the microstructural properties of the Limit Order Book (LOB) across a basket of assets with different relative tick-sizes. A key contribution of this study is the identification of several stylized facts, which are used to differentiate between large, medium, and small-tick assets, along with clear metrics for their measurement. We provide cross-asset visualizations to illustrate how these attributes vary with relative tick-size. Further, we propose a Hawkes Process model that {"\color{black"}not only fits well for large-tick assets, but also accounts for }sparsity, multi-tick level price moves, and the shape of the LOB in small-tick assets. Through simulation studies, we demonstrate the {"\color{black"} versatility} of the model and identify key variables that determine whether a simulated LOB resembles a large-tick or small-tick asset. Our tests show that stylized facts like sparsity, shape, and relative returns distribution can be smoothly transitioned from a large-tick to a small-tick asset using our model. We test this model’s assumptions, showcase its challenges and propose questions for further directions in this area of research. ...