Hawkes Processes for Order Flow Modeling

Overview

This project implements a Univariate Hawkes Process to model the arrival times of high-frequency trades (tick data). Unlike Poisson processes, which assume event independence, Hawkes processes capture the "self-exciting" nature of financial markets where a large trade increases the probability of subsequent trades.

This tool is designed to estimate the Branching Ratio ($n$), a critical metric in market microstructure that quantifies the degree of reflexivity (endogeneity) in the order book.

Key Features:

• Recursive MLE: Custom $O(N)$ Log-Likelihood implementation (vs. naive $O(N^2)$).
• Ogata's Thinning: Simulation engine for generating synthetic "flash crash" scenarios.
• Criticality Detection: Automated calculation of market stability metrics.

Mathematical Theory

The conditional intensity function $\lambda(t)$ is defined as:

$$\lambda(t) = \mu + \sum_{t_i < t} \alpha e^{-\beta(t - t_i)}$$

Where:

• $\mu$: Background intensity (exogenous events, e.g., news).
• $\alpha$: Excitation parameter (immediate impact of a trade).
• $\beta$: Decay rate (how fast the market "forgets" the trade).

The Branching Ratio ($n$) determines market stability: $$n = \frac{\alpha}{\beta}$$

• If $n &lt; 1$: Sub-critical (Stable).
• If $n \ge 1$: Super-critical (Unstable / Flash Crash Prone).

Project Structure

• src/model.py: Core Hawkes logic, including the recursive log-likelihood function.
• src/data_gen.py: Synthetic tick data generator using Ogata's Thinning Algorithm.
• src/analytics.py: Visualization tools for intensity curves and criticality reporting.

Disclaimer

Educational Use Only. This software is for research and educational purposes. It is not intended to be used as a standalone trading system or financial advice. The "Criticality" metrics derived here are theoretical constructs and may not predict all market anomalies.