GBM assumes volatility is constant. Real intraday markets don't care.
Large price moves cluster. A spike today makes another spike tomorrow significantly more likely. That's not noise — that's structure.
I built a Merton jump-diffusion model enhanced with a Hawkes self-exciting process to simulate this exactly, across a 5-asset intraday universe: AAPL, QQQ, SPY, VIX, and BTC-USD.
What's inside the full article 👇
→ Why standard GBM breaks down at the microstructure level
→ How the Hawkes process models self-exciting jump clustering
→ Full Python implementation: calibrated from live 1-min yfinance data
→ Monte Carlo path generation + visualization dashboard
→ Use cases: options desk, strategy stress-testing, crypto vol modeling
Full article + code 👇
algoedge-insights.hashnode.dev/volatility-cluster…
#python #quant #algotrading #finance
Ayrat Murtazin
I publish free Python trading notebooks every week. Grab my free starter pack of 3 ready-to-run strategies here → https://shorturl.at/WVdNF
Quick breakdown of why Hawkes matters here:
A standard Poisson process (used in classic Merton) has no memory. The probability of the next jump is the same whether a jump just happened or not.
A Hawkes process is self-exciting — each arriving event temporarily raises the rate of future events. The excitation decays exponentially: λ(t) = λ₀ + α · Σ exp(−β · (t − tᵢ))
The key constraint: α/β < 1 keeps the process stationary. Push past that and intensity explodes.
In practice, this means a single bad print can cascade — and the simulation captures exactly that.