How Well Does a Rolling-Volatility Band Calibrate?

A deliberately simple statistical envelope — a band drawn around price every bar, built from how a market has been moving over the last sixty bars.

We test it across 97 years of the S&P 500 and forty instruments spanning equities, ETFs, G10 FX, commodities, rates, and crypto. The inner band contains the next close about 71% of the time. The outer band, about 94%. Those rates stay stable across every calendar decade in the sample — the Great Depression, two world wars, the 1987 crash, the 2008 financial crisis, COVID, the AI cycle — and across asset classes that share almost no other statistical property.

The 71% is not a Gaussian quantile by accident. It's the leptokurtic fingerprint of fat-tailed returns, reproducible from first principles in a clean GARCH-with-fat-tails simulation, and stable under every robustness check we ran: out-of-sample splits, random universes, alternative source prices, weekly and monthly frequencies, and a sweep of estimation windows.

The paper also documents where the model falls short. Its calibration is marginal — it holds in the long run unconditionally — not conditional: at crisis onsets when the VIX exceeds 30, inner-band containment drops to roughly 65%. The model is a classifier of the next bar's range, not a directional forecast, not a buy/sell signal. The paper is open about that, and about every other place the model is not perfect.

Working paper. Not peer-reviewed. Comments welcome at hello@oisigma.com.