In a recent issue of The Option Strategist Newsletter, we deatailed a trading system based on a modified version of John Bollinger's Bollinger Bands. We have since received numerous inquiries asking how we calculate and plot our "modified" version. We will answer that question in this blog post, but before we do we will provide some background information on the difference between our modified version and the standard calculation. From The Option Strategist Newsletter Volume 22, Number 20:
...The following is a quick review of the indicators that are used in this system. First, as to Bollinger Bands themselves: there is a slight difference between “normal” Bollinger Bands and what we call “modified” Bollinger Bands. Both compute bands surrounding the 20-day moving average of the underlying. The width of those bands varies with volatility: the more volatile the underlying is at the time, the wider apart the bands will be.
The difference between the two results from the manner in how volatility is calculated. In the “normal” Bollinger Band calculation, volatility is the standard deviation of closing prices. In our “modified” Bollinger Band calculation, volatility is calculated as it is in the Black-Scholes model and other option modeling calculations: as the standard deviation of daily percentage price changes...
To calculate our modified version you would calculate the 20-day standard deviation of $SPX in the same was as shown in the book Options As A Strategic Investment. Then you'd plot the +4 std deviation, +3, -3 and -4 std deviation points daily, where, for example, the +4 std deviation point would be:
20-day MA * e ** (4 * stddev)
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