Bollinger bands (BBANDS) also builds on top of moving averages, but incorporates recent price volatility that makes the indicator more adaptive to different market conditions. Let's now discuss this in greater detail.

Bollinger bands is a well-known technical analysis indicator developed by John Bollinger. It computes a moving average of the prices (you can use the simple moving average or the exponential moving average or any other variant). In addition, it computes the standard deviation of the prices in the lookback period by treating the moving average as the mean price. It then creates an upper band that is a moving average, plus some multiple of standard price deviations, and a lower band that is a moving average minus multiple standard price deviations. This band represents the expected volatility of the prices by treating the moving average of the price as the reference price. Now, when prices move outside of these bands, that can be interpreted as a breakout/trend signal or an overbought/sold mean reversion signal.

Let's look at the equations to compute the upper Bollinger band, , and the lower Bollinger band, . Both depend, in the first instance, on the middle Bollinger band, , which is simply the simple moving average of the previous time periods( in this case, the last days ) denoted by. The upper and lower bands are then computed by adding/subtracting  to , which is the product of standard deviation, , which we've seen before, and , which is a standard deviation factor of our choice. The larger the value of  chosen, the greater the Bollinger bandwidth for our signal, so it is just a parameter that controls the width in our trading signal:

Here, the following applies:

: Standard deviation factor of our choice

To compute the standard deviation, first we compute the variance:

Then, the standard deviation is simply the square root of the variance: