Self-Exciting Point Processes

In financial markets, event clustering represents a fundamental challenge to classical stochastic modeling. Traditional Poisson processes assume memoryless arrivals—each trade, each order, independent of the past. Yet empirical evidence contradicts this assumption: trades cluster, volatility persists, and market microstructure exhibits clear temporal dependence.

This research examines Hawkes processes, a class of self-exciting point processes where past events increase the conditional intensity of future arrivals. Originally developed for seismology (modeling earthquake aftershocks), Hawkes processes have proven remarkably effective in capturing the clustering dynamics of high-frequency trading data.

We develop a complete mathematical framework—from first principles through maximum likelihood estimation—and validate the model against synthetic and empirical datasets. The implementation includes stability analysis, branching process interpretation, and model comparison via information criteria.

This project represents a synthesis of stochastic calculus, statistical inference, and computational implementation—demonstrating full-stack quantitative research capabilities.