Definition and Purpose:

The HistoricVolatility function calculates the realized historical volatility of a given price series over a specified number of periods. Historical volatility measures the degree of variation in the price of a financial instrument over time, expressed as a percentage. It is a useful indicator for assessing the risk associated with the price fluctuations of the asset.

Syntax:

HistoricVolatility[N](price)

Where N is the number of periods over which the volatility is calculated, and price refers to the price series (e.g., close, open, high, low).

Calculation Method:

• Select the number of periods for analysis (e.g., 20 days).
• Calculate the daily price changes within this period.
• Apply the Napierian logarithm to these price changes to stabilize variance.
• Extrapolate these values to derive the annualized percentage of historical volatility.

Example:

// Calculate the 10-period historical volatility of closing prices
i1 = HistoricVolatility[10](close)

// Calculate the 100-period moving average of i1
i2 = average[100](i1)

// Calculate the 10-period moving average of closing prices
i3 = average[10](close)

// Define trading signals based on volatility and price averages
IF (i1 > i2 AND Close < i3) THEN
    bearish = -1
    bullish = 0
ELSIF (i1 > i2 AND Close > i3) THEN
    bearish = 0
    bullish = 1
ELSE
    bearish = 0
    bullish = 0
ENDIF

RETURN bearish, bullish

This example demonstrates how to use the HistoricVolatility function to generate trading signals based on comparisons between current volatility, its longer-term average, and the current price relative to its short-term average.

Additional Information:

Historical volatility is distinct from implied volatility, which is a forward-looking metric derived from the market price of a derivative (particularly options). Historical volatility is calculated from actual past price movements and is therefore considered a factual, observed value.