Microstructure

Boltzmann Price: Toward Understanding the Fair Price in High-Frequency Markets ArXiv ID: 2507.09734 “View on arXiv” Authors: Przemysław Rola Abstract In this paper, we introduce a parametrized family of prices derived from the Maximum Entropy Principle. The price is obtained from the distribution that minimizes bias, given the bid and ask volume imbalance at the top of the order book. Under specific parameter choices, it closely approximates the mid-price or the weighted mid-price. Using probabilities of bid and ask states, we propose a model of price dynamics in which both drift and volatility are driven by volume imbalance. Compared to standard models like Bachelier or Geometric Brownian Motion with constant volatility, our model can generate higher kurtosis and heavy-tailed distributions. Additionally, the drift term naturally emerges as a consequence of the order book imbalance. We validate the model through simulation and demonstrate its fit to historical equity data. The model provides a theoretical framework, integrating price, volume imbalance, and spread. ...

Risk-Adjusted Performance of Random Forest Models in High-Frequency Trading ArXiv ID: 2412.15448 “View on arXiv” Authors: Unknown Abstract Because of the theoretical challenges posed by the Efficient Market Hypothesis to technical analysis, the effectiveness of technical indicators in high-frequency trading remains inadequately explored, particularly at the minute-level frequency, where effects of the microstructure of the market dominate. This study evaluates the integration of traditional technical indicators with random forest regression models using minute-level SPY data, analyzing 13 distinct model configurations. Our empirical results reveal a stark contrast between in-sample and out-of-sample performance, with $R^2$ values deteriorating from 0.749–0.812 during training to negative values in testing. A feature importance analysis demonstrates that primary price-based features dominate the predictions made by the model, accounting for over 60% of the importance, while established technical indicators, such as RSI and Bollinger Bands, account for only 14%–15%. Although the indicator-enhanced models achieved superior risk-adjusted metrics, with Rachev ratios between 0.919 and 0.961, they consistently underperformed a simple buy-and-hold strategy, generating returns ranging from -2.4% to -3.9%. These findings challenge conventional assumptions about the usefulness of technical indicators in algorithmic trading, suggesting that in high-frequency contexts, they may be more relevant to risk management rather than to predicting returns. For practitioners and researchers, our findings indicate that successful high-frequency trading strategies should focus on adaptive feature selection and regime-specific modeling rather than relying on traditional technical indicators, as well as indicating the critical importance of robust out-of-sample testing in the development of a model. ...

How does liquidity shape the yield curve? ArXiv ID: 2409.12282 “View on arXiv” Authors: Unknown Abstract The phenomenology of the forward rate curve (FRC) can be accurately understood by the fluctuations of a stiff elastic string (Le Coz and Bouchaud, 2024). By relating the exogenous shocks driving such fluctuations to the surprises in the order flows, we elevate the model from purely describing price variations to a microstructural model that incorporates the joint dynamics of prices and order flows, accounting for both impact and cross-impact effects. Remarkably, this framework allows for at least the same explanatory power as existing cross-impact models, while using significantly fewer parameters. In addition, our model generates liquidity-dependent correlations between the forward rate of one tenor and the order flow of another, consistent with recent empirical findings. We show that the model also account for the non-martingale behavior of prices at short timescales. ...

HLOB – Information Persistence and Structure in Limit Order Books ArXiv ID: 2405.18938 “View on arXiv” Authors: Unknown Abstract We introduce a novel large-scale deep learning model for Limit Order Book mid-price changes forecasting, and we name it `HLOB’. This architecture (i) exploits the information encoded by an Information Filtering Network, namely the Triangulated Maximally Filtered Graph, to unveil deeper and non-trivial dependency structures among volume levels; and (ii) guarantees deterministic design choices to handle the complexity of the underlying system by drawing inspiration from the groundbreaking class of Homological Convolutional Neural Networks. We test our model against 9 state-of-the-art deep learning alternatives on 3 real-world Limit Order Book datasets, each including 15 stocks traded on the NASDAQ exchange, and we systematically characterize the scenarios where HLOB outperforms state-of-the-art architectures. Our approach sheds new light on the spatial distribution of information in Limit Order Books and on its degradation over increasing prediction horizons, narrowing the gap between microstructural modeling and deep learning-based forecasting in high-frequency financial markets. ...