Willy Bands

Reverse engineered Willy21Ema13 to show (on chart) the levels price would have to reach to be overbought/oversold given recent price history.
By default it only shows the Williams%R with length 21.
If you change the settings it will do the same for the Ema13 of the Willy21, however because the ema is "harder" to breach, the lines are much farther away and looks really obnoxious on chart.
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study(title="Willy Bands", overlay=true)
// Created by GunArm July 6 2014
// Not exactly Groundbreaking, but hey ;p
// Thanks MagnusTradingGroup, LazyBear, and lucky_Hard for suggestions

willyLength = input(21, title="Williams Length", minval=1) 
ob_level = input(-20, title="Overbought level", minval=-100, maxval=0)
os_level = input(-80, title="Oversold level",  minval=-100, maxval=0)
noEma = input(title="Williams%R only (no EMA)", type=bool, defval=true)
emaLength = input(13, title="Ema Length", minval=1) 

upper = highest(willyLength)
lower = lowest(willyLength)
alpha = 2/(emaLength + 1)

currentWillyEma = ema(100 * (close - upper) / (upper - lower), emaLength)

InverseWilly(result) => upper + (result * (upper - lower)/100)
InverseEma(currentEma, targetEma) => ((targetEma - currentEma)/alpha) + currentEma

ob_Willy = InverseWilly(ob_level)
ob_WillyEma = InverseWilly(InverseEma(currentWillyEma, ob_level))

os_Willy = InverseWilly(os_level)
os_WillyEma = InverseWilly(InverseEma(currentWillyEma, os_level))

plot(noEma ? ob_Willy : ob_WillyEma, color = red)
plot(noEma ? os_Willy : os_WillyEma, color = green)
very usefull tool - Thank You / use it on all timeframes for showing overbought/oversold levels
this man is a genius. huge props. thank you !
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