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| **PineScript** | [bbands.pine](bbands.pine) |
- Bollinger Bands construct a volatility-adaptive envelope around a Simple Moving Average using population standard deviation as the width measure.
- **Similar:** [KChannel](../kchannel/kchannel.md), [SDChannel](../sdchannel/sdchannel.md), [ABERR](../aberr/aberr.md) | **Complementary:** %B and BandWidth for squeeze detection; RSI for momentum confirmation | **Trading note:** Most widely used band indicator; 2s captures ~95% of normally-distributed data but markets exhibit fat tails.
- **Similar:** [KC](../kc/kc.md), [SDChannel](../sdchannel/sdchannel.md), [ABERR](../aberr/aberr.md) | **Complementary:** %B and BandWidth for squeeze detection; RSI for momentum confirmation | **Trading note:** Most widely used band indicator; 2s captures ~95% of normally-distributed data but markets exhibit fat tails.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
Bollinger Bands construct a volatility-adaptive envelope around a Simple Moving Average using population standard deviation as the width measure. The bands expand during high-volatility periods and contract during consolidation, dynamically adapting to changing market conditions. Under Gaussian assumptions, $\pm 2\sigma$ contains approximately 95.4% of price action, but financial returns exhibit fat tails and volatility clustering, so the bands function more as a volatility-normalized reference frame than a strict probability envelope. The derived metrics %B (price position as a fraction of band width) and BandWidth (normalized band spread) extend the raw bands into a complete analytical toolkit.