Bollinger BandWidth (BBW)

Summary

Bollinger BandWidth: the distance between the upper and lower Bollinger Bands as a percentage of the middle band. Low values mark contracting volatility, the setup John Bollinger calls the Squeeze; high values mark expanding volatility.

Formula

$$\mathrm{BBW}_t = 100 \cdot \frac{\mathrm{upper}_t - \mathrm{lower}_t}{\mathrm{middle}_t}, \text{ or } 0 \text{ when } \mathrm{middle}_t = 0$$

where $\mathrm{upper}_t$, $\mathrm{middle}_t$ and $\mathrm{lower}_t$ are the BBANDS bands of $X$ with period $n$, moving-average type $\text{matype}$ and deviation multipliers $k_{\text{up}}$, $k_{\text{dn}}$. Since both bands sit on the middle band, $\mathrm{BBW}_t = 100\,(k_{\text{up}} + k_{\text{dn}})\,\sigma_t / \mathrm{middle}_t$, with $\sigma_t$ the population standard deviation of the last $n$ values of $X$.

Notes

• With Bollinger's settings (a simple moving average and two deviations on each side) BBW is 400 times the window's coefficient of variation: its standard deviation divided by its mean.
• The two deviation multipliers enter only through their sum.
• The result is in percent: 10 means the bands are 10% of the middle band apart.
• Any optInMAType other than SMA is a TA-Lib generalisation, as it is for BBANDS: the deviation stays the population standard deviation about the simple mean.
• Wherever the middle band is not 0, BBW is bit for bit ((upper - lower) / middle) * 100 computed from BBANDS' own outputs.

Inputs

• inReal — Input data series

Outputs

• outReal — Width of the bands as a percentage of the middle band

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	20	2–100000	Periods for the MA and standard deviation
optInNbDevUp	real	2	any real	Standard-deviation multiplier for the upper band
optInNbDevDn	real	2	any real	Standard-deviation multiplier for the lower band
optInMAType	MAType	SMA (0)	any MAType	Moving-average type for the middle band

MAType values: 0 SMA · 1 EMA · 2 WMA · 3 DEMA · 4 TEMA · 5 TRIMA · 6 KAMA · 7 MAMA · 8 T3 · 9 HMA · 10 DISABLED · 11 DEFAULT · 12 ZLEMA · 13 RMA · 14 VIDYA · 15 ALMA

Properties

Numerical Stability: Depends on MA Type — This function's default, SMA, is start-independent.

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: bbw.c · bbw.yaml

Native	File
C	ta_BBW.c
Rust	bbw.rs
Java	Core_BBW.java
C#	Core_BBW.cs

TA-Lib is also available for Python, R and more using a wrapper.

Aliases

Bollinger BandWidth, Bollinger Band Width, Bollinger Bands Width, BandWidth

See Also

BBANDS · PERCENTB · STDDEV · NATR

References

• John A. Bollinger, Bollinger on Bollinger Bands, McGraw-Hill 2001 (ISBN 0071373683)
• John Bollinger, Bollinger Band Rules, rule 18