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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.

April 14, 2026 | Reading Time: 5 minutes arch models

For decades, standard statistical models assumed something called homoscedasticity —a fancy way of saying "constant variance." But financial returns are clearly heteroscedastic (changing variance). April 14, 2026 | Reading Time: 5 minutes

This matches reality. After the COVID crash in March 2020, the VIX (fear index) stayed above 25 for nearly six months. 1. Risk Management If you assume volatility is constant, your Value at Risk (VaR) will be wrong 90% of the time. GARCH models give you dynamic VaR—higher during crises, lower during calm periods. The equation looks intimidating

The equation looks intimidating, but it’s just a weighted average of past surprises:

[ \sigma_t^2 = \omega + \alpha \epsilon_t-1^2 + \beta \sigma_t-1^2 ]

If you have ever tried to predict stock market volatility, you have run into a frustrating reality: