The middle band is a moving average used to establish the intermediate-term trend. The 3 upper bands are constructed by using the Wilders Smoothed ATR and multiplying it by each of the Fibonacci factors (1.618, 2.618, and 4.236) and then adding the results to the middle band. The 3 lower bands are constructed in the same manner as the upper bands except their results are subtracted from the middle band.
In true TradingView spirit, the author of this script has published it open-source, so traders can understand and verify it. Cheers to the author! You may use it for free, but reuse of this code in a publication is governed by House Rules. You can favorite it to use it on a chart.
//@version=2 study("Bollingers Bands Fibonacci ratios",shorttitle="FiBB",overlay=true) len=input(defval=20,minval=1) p=close sma=sma(p,len) avg=atr(len) fibratio1=input(defval=1.618,title="Fibonacci Ratio 1") fibratio2=input(defval=2.618,title="Fibonacci Ratio 2") fibratio3=input(defval=4.236,title="Fibonacci Ratio 3") r1=avg*fibratio1 r2=avg*fibratio2 r3=avg*fibratio3 top3=sma+r3 top2=sma+r2 top1=sma+r1 bott1=sma-r1 bott2=sma-r2 bott3=sma-r3 t3=plot(top3,transp=0,title="Upper 3",color=teal) t2=plot(top2,transp=20,title="Upper 2",color=teal) t1=plot(top1,transp=40,title="Upper 1",color=teal) b1=plot(bott1,transp=40,title="Lower 1",color=teal) b2=plot(bott2,transp=20,title="Lower 2",color=teal) b3=plot(bott3,transp=0,title="Lower 3",color=teal) plot(sma,style=cross,title="SMA",color=teal) fill(t3,b3,color=navy,transp=85)