Is the Bollinger Bands assumption wrong?

Bitcoin / United States DollarCoinbase

설명

⋅ 2022년 5월 3일 오후 9시 38분

Bollinger Bands are the result of the assumption that closing prices will follow a normal distribution.

However, when I actually calculated the probability, the closing price does not follow a normal distribution.

According to the normal distribution, the probability that Z > 2 should be 2.2%, but on the chart, the probability is 6~9%.

Can we get a useful value for Bollinger Bands that we can use in our strategy?

We can measure volatility, but can we judge volatility based on a fixed value?

To the right of each Bollinger band value, the probability that the price is above the band is displayed.

The script is simply annotated with how each probability is calculated.

Bollinger Bands (BB)normaldistribution

코멘트

Trendoscope

⋅ 2022년 5월 11일 오전 11시 33분

I think the probability depends on the instrument. Trending instrument may have completely different picture. I am also unsure if it is recorded anywhere about this use case. There is a video by John Bollinger where he explains how he use Bollinger bands. That doesn’t talk about probability distribution at all.

Dicargo_Beam

⋅ 2022년 5월 11일 오후 3시 20분

@HeWhoMustNotBeNamed, Oh, I thought that the mathematical expression of Bollinger Bands was derived from the normal distribution in that it was the same as the standardization of the normal distribution.

Trendoscope

⋅ 2022년 5월 12일 오전 8시 21분

@Dicargo_Beam,

Upper band = MA + 2* Standard deviation
Lower band = MA - 2*Standard deviation

I take it as just measure of volatility. May be I am bit illiterate about stats. Let me also attempt a script. But, in slightly different way.