Enhancing Bivariate Hawkes Processes for High-Frequency Trading
Bibliographic record
Abstract
High-Frequency Trading (HFT) relies on the precise modeling of order book dynamics to effectively predict market movements. The Bivariate Hawkes Process (BHP) is widely used in HFT to capture self-excitation and cross-excitation between order arrivals. However, standard BHP models struggle to incorporate real-time liquidity and volatility patterns. This study introduces an Enhanced BHP (E-BHP) framework that integrates a Liquidity Imbalance Factor (OBI) and Rolling Standard Deviation of Price Movements (HV) to improve predictive accuracy. Additionally, we introduce adaptive weight parameters α and β to dynamically adjust the model sensitivity to market fluctuations.Unlike simple additive inclusion, the OBI and HV components are incorporated within the conditional intensity function, modifying the excitation kernel to reflect market state-dependent effects. This approach preserves the theoretical structure of the Hawkes process while enabling dynamic responsiveness.The parameters α and β are treated as trainable hyperparameters and optimized using grid search over validation folds during cross-validation. This ensures they are tuned to balance the influence of OBI and HV on event intensity without overfitting.Empirical results using NASDAQ limit order book data demonstrate that our enhanced model reduces prediction error, improving the RMSE from 0.7208 to 0.0169 and $\mathbf{R}^{2}$ from 0.5666 to 0.7000, thereby outperforming the traditional BHP. The evaluation was conducted using a cross-validation strategy to ensure robustness. While the performance gains are substantial, further assessment under diverse market conditions is necessary to validate generalisability. These enhancements make the E-BHP a valuable tool for market microstructure analysis, execution optimization, and risk-aware trading strategies.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.011 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".