# Bollinger Bands

Submitted by kolier on Sun, 05/16/2010 - 20:07

#### History

Bollinger Bands is a technical analysis tool invented by John Bollinger in the 1980s.

#### Purpose

Bollinger Bands tries to use statistic manner to utilize history price data to predict the fluctuation high and low in the future market.

#### Logic

Bollinger Bands contains three lines:

**Center**is the simple moving average of the close price of the bar. Default uses 20 period. Center = SMA(Price_Close, Period)**Upper**is k(default 2) times deviation of the center line above. Random variable subject is Close price of the bar. Upper = Center + k*Dev(Price_Close)**Lower**is k times deviation of the center line below. Random variable subject is Close price of the bar. Lower = Center - k*Dev(Price_Close)

#### Maths Support - Bollinger Bands Secret

BB make center line as the expectation of close of the bar.

Apply the Chebyshev's Inequality, we know the probability of the close price cross above the upper line (or cross below the lower line).

When we use default 2 deviation settings. This probability is *TeX Embedding failed!*(25%).