Hawkes Processes

Analysis of Contagion in China’s Stock Market: A Hawkes Process Perspective ArXiv ID: 2512.08000 “View on arXiv” Authors: Junwei Yang Abstract This study explores contagion in the Chinese stock market using Hawkes processes to analyze autocorrelation and cross-correlation in multivariate time series data. We examine whether market indices exhibit trending behavior and whether sector indices influence one another. By fitting self-exciting and inhibitory Hawkes processes to daily returns of indices like the Shanghai Composite, Shenzhen Component, and ChiNext, as well as sector indices (CSI Consumer, Healthcare, and Financial), we identify long-term dependencies and trending patterns, including upward, downward, and oversold rebound trends. Results show that during high trading activity, sector indices tend to sustain their trends, while low activity periods exhibit strong sector rotation. This research models stock price movements using spatiotemporal Hawkes processes, leveraging conditional intensity functions to explain sector rotation, advancing the understanding of financial contagion. ...

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 ...

ARL-Based Multi-Action Market Making with Hawkes Processes and Variable Volatility ArXiv ID: 2508.16589 “View on arXiv” Authors: Ziyi Wang, Carmine Ventre, Maria Polukarov Abstract We advance market-making strategies by integrating Adversarial Reinforcement Learning (ARL), Hawkes Processes, and variable volatility levels while also expanding the action space available to market makers (MMs). To enhance the adaptability and robustness of these strategies – which can quote always, quote only on one side of the market or not quote at all – we shift from the commonly used Poisson process to the Hawkes process, which better captures real market dynamics and self-exciting behaviors. We then train and evaluate strategies under volatility levels of 2 and 200. Our findings show that the 4-action MM trained in a low-volatility environment effectively adapts to high-volatility conditions, maintaining stable performance and providing two-sided quotes at least 92% of the time. This indicates that incorporating flexible quoting mechanisms and realistic market simulations significantly enhances the effectiveness of market-making strategies. ...

Order-Flow Filtration and Directional Association with Short-Horizon Returns ArXiv ID: 2507.22712 “View on arXiv” Authors: Aditya Nittur Anantha, Shashi Jain, Prithwish Maiti Abstract Electronic markets generate dense order flow with many transient orders, which degrade directional signals derived from the limit order book (LOB). We study whether simple structural filters on order lifetime, modification count, and modification timing sharpen the association between order book imbalance (OBI) and short-horizon returns in BankNifty index futures, where unfiltered OBI is already known to be a strong short-horizon directional indicator. The efficacy of each filter is evaluated using a three-step diagnostic ladder: contemporaneous correlations, linear association between discretised regimes, and Hawkes event-time excitation between OBI and return regimes. Our results indicate that filtration of the aggregate order flow produces only modest changes relative to the unfiltered benchmark. By contrast, when filters are applied on the parent orders of executed trades, the resulting OBI series exhibits systematically stronger directional association. Motivated by recent regulatory initiatives to curb noisy order flow, we treat the association between OBI and short-horizon returns as a policy-relevant diagnostic of market quality. We then compare unfiltered and filtered OBI series, using tick-by-tick data from the National Stock Exchange of India, to infer how structural filters on the order flow affect OBI-return dynamics in an emerging market setting. ...

Event-Time Anchor Selection for Multi-Contract Quoting ArXiv ID: 2507.05749 “View on arXiv” Authors: Aditya Nittur Anantha, Shashi Jain, Shivam Goyal, Dhruv Misra Abstract When quoting across multiple contracts, the sequence of execution can be a key driver of implementation shortfall relative to the target spread~\cite{“bergault2022multi”}. We model the short-horizon execution risk from such quoting as variations in transaction prices between the initiation of the first leg and the completion of the position. Our quoting policy anchors the spread by designating one contract ex ante as a \emph{“reference contract”}. Reducing execution risk requires a predictive criterion for selecting that contract whose price is most stable over the execution interval. This paper develops a diagnostic framework for reference-contract selection that evaluates this stability by contrasting order-flow Hawkes forecasts with a Composite Liquidity Factor (CLF) of instantaneous limit order book (LOB) shape. We illustrate the framework on tick-by-tick data for a pair of NIFTY futures contracts. The results suggest that event-history and LOB-state signals offer complementary views of short-horizon execution risk for reference-contract selection. ...

Learning the Spoofability of Limit Order Books With Interpretable Probabilistic Neural Networks ArXiv ID: 2504.15908 “View on arXiv” Authors: Unknown Abstract This paper investigates real-time detection of spoofing activity in limit order books, focusing on cryptocurrency centralized exchanges. We first introduce novel order flow variables based on multi-scale Hawkes processes that account both for the size and placement distance from current best prices of new limit orders. Using a Level-3 data set, we train a neural network model to predict the conditional probability distribution of mid price movements based on these features. Our empirical analysis highlights the critical role of the posting distance of limit orders in the price formation process, showing that spoofing detection models that do not take the posting distance into account are inadequate to describe the data. Next, we propose a spoofing detection framework based on the probabilistic market manipulation gain of a spoofing agent and use the previously trained neural network to compute the expected gain. Running this algorithm on all submitted limit orders in the period 2024-12-04 to 2024-12-07, we find that 31% of large orders could spoof the market. Because of its simple neuronal architecture, our model can be run in real time. This work contributes to enhancing market integrity by providing a robust tool for monitoring and mitigating spoofing in both cryptocurrency exchanges and traditional financial markets. ...

Mean-Field Limits for Nearly Unstable Hawkes Processes ArXiv ID: 2501.11648 “View on arXiv” Authors: Unknown Abstract In this paper, we establish general scaling limits for nearly unstable Hawkes processes in a mean-field regime by extending the method introduced by Jaisson and Rosenbaum. Under a mild asymptotic criticality condition on the self-exciting kernels ${“φ^n"}$, specifically $|φ^n|{“L^1”} \to 1$, we first show that the scaling limits of these Hawkes processes are necessarily stochastic Volterra diffusions of affine type. Moreover, we establish a propagation of chaos result for Hawkes systems with mean-field interactions, highlighting three distinct regimes for the limiting processes, which depend on the asymptotics of $n(1-|φ^n|{“L^1”})^2$. These results provide a significant generalization of the findings by Delattre, Fournier and Hoffmann. ...

Optimal Execution under Incomplete Information ArXiv ID: 2411.04616 “View on arXiv” Authors: Unknown Abstract We study optimal liquidation strategies under partial information for a single asset within a finite time horizon. We propose a model tailored for high-frequency trading, capturing price formation driven solely by order flow through mutually stimulating marked Hawkes processes. The model assumes a limit order book framework, accounting for both permanent price impact and transient market impact. Importantly, we incorporate liquidity as a hidden Markov process, influencing the intensities of the point processes governing bid and ask prices. Within this setting, we formulate the optimal liquidation problem as an impulse control problem. We elucidate the dynamics of the hidden Markov chain’s filter and determine the related normalized filtering equations. We then express the value function as the limit of a sequence of auxiliary continuous functions, defined recursively. This characterization enables the use of a dynamic programming principle for optimal stopping problems and the determination of an optimal strategy. It also facilitates the development of an implementable algorithm to approximate the original liquidation problem. We enrich our analysis with numerical results and visualizations of candidate optimal strategies. ...

Forecasting High Frequency Order Flow Imbalance ArXiv ID: 2408.03594 “View on arXiv” Authors: Unknown Abstract Market information events are generated intermittently and disseminated at high speeds in real-time. Market participants consume this high-frequency data to build limit order books, representing the current bids and offers for a given asset. The arrival processes, or the order flow of bid and offer events, are asymmetric and possibly dependent on each other. The quantum and direction of this asymmetry are often associated with the direction of the traded price movement. The Order Flow Imbalance (OFI) is an indicator commonly used to estimate this asymmetry. This paper uses Hawkes processes to estimate the OFI while accounting for the lagged dependence in the order flow between bids and offers. Secondly, we develop a method to forecast the near-term distribution of the OFI, which can then be used to compare models for forecasting OFI. Thirdly, we propose a method to compare the forecasts of OFI for an arbitrarily large number of models. We apply the approach developed to tick data from the National Stock Exchange and observe that the Hawkes process modeled with a Sum of Exponential’s kernel gives the best forecast among all competing models. ...

Price-Aware Automated Market Makers: Models Beyond Brownian Prices and Static Liquidity ArXiv ID: 2405.03496 “View on arXiv” Authors: Unknown Abstract In this paper, we introduce a suite of models for price-aware automated market making platforms willing to optimize their quotes. These models incorporate advanced price dynamics, including stochastic volatility, jumps, and microstructural price models based on Hawkes processes. Additionally, we address the variability in demand from liquidity takers through models that employ either Hawkes or Markov-modulated Poisson processes. Each model is analyzed with particular emphasis placed on the complexity of the numerical methods required to compute optimal quotes. ...