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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.

Beyond the White Noise: Why Financial Markets Need ARCH and GARCH 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). arch models

April 14, 2026 | Reading Time: 5 minutes

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

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.

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. Risk Management If you assume volatility is constant,

Yet, until Robert Engle introduced ARCH in 1982 (earning him the 2003 Nobel Prize), most econometric models did exactly that for financial data.