The Black-Scholes model assumes constant volatility—which traders know is false. GARCH-based option pricing models (e.g., Heston-Nandi) better capture the volatility smile.
Enter (introduced by Tim Bollerslev in 1986). A GARCH(1,1) model—the industry workhorse—uses only three parameters to capture volatility dynamics: arch models
The equation looks intimidating, but it’s just a weighted average of past surprises: April 14, 2026 | Reading Time: 5 minutes
This is where (Autoregressive Conditional Heteroskedasticity) and its big brother GARCH (Generalized ARCH) come to save the day. The Problem with "Constant Volatility" Imagine trying to forecast tomorrow's temperature using a model that assumes the weather has the same variability in July as it does in December. That would be absurd. arch models
April 14, 2026 | Reading Time: 5 minutes
If you have ever tried to predict stock market volatility, you have run into a frustrating reality: