Bollinger Bands (BOLL) consist of three lines that measure voltaility and price dynamics over time.

Mathematical Definition

• Middle Band: N-period Simple Moving Average (SMA) of closing prices, typically using N=20.
• Upper Band: Middle Band + K multiplied by the N-period standard deviation, typically K=2.
• Lower Band: Middle Band - M multiplied by the N-period standard deviation, typically M=2.

Python Implementation

Custom Calculation

Using a custom function with pandas allows for flexibility, particularly when aligning with specific regional trading platform standards.

import pandas as pd

def compute_bollinger(data_frame, window=20, upper_factor=2, lower_factor=2):
    sorted_frame = data_frame.sort_values('timestamp')
    price_col = sorted_frame['closing_price']
    
    moving_avg = price_col.rolling(window=window).mean()
    # Using ddof=0 for population standard deviation (dividing by N)
    price_volatility = price_col.rolling(window=window).std(ddof=0)
    
    sorted_frame['middle_band'] = moving_avg
    sorted_frame['upper_band'] = moving_avg + (upper_factor * price_volatility)
    sorted_frame['lower_band'] = moving_avg - (lower_factor * price_volatility)
    
    return sorted_frame

TA-Lib Implementation

The TA-Lib library provides a highly optimized built-in function for Bollinger Bands.

import talib as ta
import pandas as pd

upper_band, middle_band, lower_band = ta.BBANDS(
    data_frame['closing_price'],
    timeperiod=20,
    nbdevup=2,
    nbdevdn=2,
    matype=0
)

bands_df = pd.DataFrame({
    'upper_band': upper_band,
    'middle_band': middle_band,
    'lower_band': lower_band
})

combined_data = pd.concat([data_frame, bands_df], axis=1)

Standard Deviation Discrepancy

A numerical difference exists between the custom pandas calculation and the TA-Lib output due to how standard deviation is computed.

Domestic securities platforms typical display Bollinger Bands based on population standard deviation. To replicate this behavior in pandas, explicitly set ddof=0 in the .std() method; otherwise, pandas defaults to sample standard deviation (ddof=1).