Historical Volatility

Historical volatility is a measure of volatility over a fixed span of time.

Historical volatility is calculated by taking the standard deviation of the natural log of the ratio of consecutive closing prices over time.  This is multiplied by the square root of the number of bars in a year so it can be compared to other time spans and multiplied by 100 to convert it to a percentage.

Custom PCF Formula
1600 * ABS((SUM(LOG(C / C1) ^ 2, x) - LOG(C / Cx) ^ 2 / x) / x) ^ .5 x=Period

Where x is the period which must be an integer.

/// <desc>Historical volatility is a measure of volatility over a fixed span of time. Historical volatility is calculated by taking the standard deviation of the natural log of the ratio of consecutive closing prices over time.  This is multiplied by the square root of the number of bars in a year so it can be compared to other time spans and multiplied by 100 to convert it to a percentage.</desc>
/// <tag>indicator</tag>
param #Period = 100 /// <desc>Number of bars over which the Historical Volatility is being calculated.</desc>
param #BarsPerYear = 256 /// <desc>The number of bars in a year in the time frame in which the Historical Volatility is being calculated. You can substitute one of the following constants in place of 256 or enter the number of bars directly.</desc>
const #Daily = 253
const #Weekly = 52
const #Monthly = 12
 100 * Sqr(#BarsPerYear) * Abs((Sum(Log(C / C1) ^ 2, #Period) - Log(C / C#Period) ^ 2 / #Period) / #Period) ^ .5
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This indicator template will only work correctly when applied to a chart template with the corresponding timeframe, by default it is set to 256 bars which equates to the daily timeframe but can be changed  by substituting the #BarsPerYear parameter value with one of the following constants in place of 256:
#Daily
#Weekly
#Monthly

or you can enter the number of bars directly into the #BarsPerYear parameter if you do not want to use one of those constants. 

The default  256 bars per year is chosen more for being an even square as being the most accurate number of daily bars in the average year. Most people use between 250 and 260 for the average number of bars in a year, so 256 should be fine.

If the formula is used with a weekly time frame for example you could use 721 or the above #Weekly constant instead even though there is a fraction of a week more than 52 weeks in a year.

Examples of the flat formula

A 6 period Historical Volatility for a daily time frame can be written as follows.

1600 * ABS((SUM(LOG(C / C1) ^ 2, 6) - LOG(C / C6) ^ 2 / 6) / 6) ^ .5

A 100 period Historical Volatility for a daily time frame can be written as follows.

1600 * ABS((SUM(LOG(C / C1) ^ 2, 100) - LOG(C / C100) ^ 2 / 100) / 100) ^ .5