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Creator of Bollinger Bands: John Bollinger (early 1980s)

The purpose of Bollinger Bands is to provide a relative definition of high and low. By definition prices are high at the upper band and low at the lower band.

Bollinger Bands are akin to envelopes on the upper and lower side of a moving average line. They consist of three curves:
Middle Curve: usually a simple moving average (SMA) of the stock price
Upper Curve: SMA + 2 standard deviations
Lower Curve: SMA – 2 standard deviations

For the moving average calculation, a period of 20 days is usually used.

Standard Deviation
Standard deviation is a statistical concept that is often used to measure stock price volatility. It also shows the spread of the stock price around its mean (or average). In the Central Limits Theorem (a Statistical Theory), a set of data will form a Normal Distribution Curve and 95.4% of the values in the data set occurring within 2 standard deviations of the mean.

Expressed in another way, there is a 95.4% probability in theory that the share price will occur within 2 standard deviations of the mean price.

The interval between the upper and lower bands and the middle band is determined by volatility, typically the standard deviation of the same data that were used for the average. The default parameters, 20 periods and two standard deviations, may be adjusted to suit your purposes.

Using Bollinger Bands
Some important concepts are used in Bollinger Bands:

1. Band Width

= (Upper Band – Lower Band) / Middle Band

The bands will expand and contract as the price action becomes volatile (expansion) or becomes bound into a tight trading pattern (contraction).

2. The Upper and Lower Bands can be used to determine price targets

Bollinger Bands can help determine overbought and oversold levels. As seen above, statistical theory has it that 95.4% of the values in a data set will occur within 2 standard deviations of the mean. When the share price move closer to the Upper Band, it indicates that the share is overbought. Conversely as the prices move closer to the lower band, it becomes oversold. Basically there is 95.4% chance that it remains within the band.

3. %b – This is a measure of where the stock price is in relation to the bands.

%b = (Price – Lower Band) / (Upper Band – Lower Band)

4. If the price deflects off the lower band and crosses above the 20-day moving average, the upper band represents the upper price target. In a strong uptrend, prices usually fluctuate between the upper band and the 20-day moving average. When that happens, a crossing below the 20-day moving average warns of a trend reversal to the downside.

Simple Illustration
A Price and Bollinger Band plot for Bursa Malaysia share price. The brown line is the 20-Day Moving Average. Notice the share price became more volatile from early-mid October. The lower most chart showing the band width also starts to move up.

The share price nears the Upper Band in early November and but the RSI does not confirm the upward move (moves closer to 70) - a sell signal is generated.