A Poisson process has a constant arrival rate — events don't care about the past. Markets aren't like that: a trade makes the next trade more likely, an order triggers a cascade. A Hawkes process captures this with an intensity that jumps up at every event and decays between them.
The conditional intensity (instantaneous arrival rate given the history) is
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Lesson close · Hawkes Processes & Market Microstructure
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Sequence
Continue to Hawkes-Driven Jump Diffusion & Volatility Clustering, the next prerequisite step in this course.
The standard choice is an exponential kernel:
Every event adds to the intensity, which then decays at rate . So bursts beget bursts — and then quiet returns.
Each event spawns, on average,
"offspring" events. This branching ratio must satisfy for the process to be stable (otherwise activity explodes). Read as the fraction of activity that is endogenous — self-generated by the market rather than driven by outside news. Empirically is high (often –) in liquid markets: most activity is the market reacting to itself.
Hawkes processes reproduce volatility clustering and trade clustering that Poisson models can't. The next lessons plug this intensity into a jump-diffusion price and into the order book.
Free preview of the Hawkes & Microstructure course.
Based on Ibrahim Lanre Adedimeji’s “Hawkes Processes: A Stochastic Gem.”
Interactive · Hawkes intensity / branching ratio
branching n=α/β=0.667 (stable) · events≈0
Knowledge check
Q1. For stability of a Hawkes process with kernel αe^(−βt), the branching ratio n = α/β must satisfy…
Q2. A branching ratio measured at n ≈ 0.9 tells you that market activity is mostly…
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