Bollinger Bands

Volatility envelope around a moving average.

Bollinger Bands, designed by John Bollinger in the 1980s, wrap a moving average (typically 20-period SMA) with an upper and lower band placed k standard deviations away (k = 2 is the default). The bands widen when volatility rises and contract when it falls — a 'squeeze' often precedes a directional move.

Typical reads: price touching the upper band in a strong uptrend is not by itself a sell signal — it is a sign of trend strength. Conversely, repeated touches outside the bands followed by a close back inside are sometimes used as mean-reversion triggers.

Because the bands are derived from the rolling standard deviation of price, they assume returns are approximately normal locally. In practice fat-tailed crypto returns regularly print outside the ±2σ band more often than the 5% Gaussian theory would predict.

Middle = SMA(N)
Upper = Middle + k · stdev(close, N)
Lower = Middle − k · stdev(close, N)

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