Next time you see a market flash crash or a sudden calm, remember: it’s not randomness. It’s conditional heteroskedasticity in action. Have you used GARCH models in production? Or do you prefer modern alternatives like stochastic volatility or deep learning? Let me know in the comments.
The equation looks intimidating, but it’s just a weighted average of past surprises: arch models
But an ARCH model recognizes a pattern: Large errors tend to be followed by large errors of either sign. At its core, an ARCH(q) model says: Today's variance depends on the squared "shocks" (unexpected returns) from the previous q days. In simple terms: If the market has been crazy for the last week, tomorrow will probably also be crazy. Next time you see a market flash crash
For decades, standard statistical models assumed something called homoscedasticity —a fancy way of saying "constant variance." But financial returns are clearly heteroscedastic (changing variance). Or do you prefer modern alternatives like stochastic
Big moves tend to be followed by big moves (in either direction), and quiet periods tend to be followed by quiet periods. If you plot the S&P 500 or Bitcoin returns, you don’t see random scatter. You see pockets of chaos and pockets of calm.
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.
April 14, 2026 | Reading Time: 5 minutes