Units of Normal Volatility and Variance

Summary

Normal volatility is measured in the same units as the underlying changes used to estimate it. In the example, realized normal volatility is calculated as the standard deviation of absolute daily changes; for an index, the result is expressed in index points. For a foreign exchange series, the corresponding unit would follow the convention used for the changes, such as pips or another quoted price unit.

Variance has squared units, while standard deviation returns to the original unit after taking the square root. The example annualizes a daily estimate using a trading-day factor, which changes its scale over time but does not change the underlying measurement unit. These interpretations assume the volatility is computed from absolute price changes; percentage or log-return volatility would instead be dimensionless or expressed according to that return convention.

Key ideas

• Normal volatility has the same measurement units as the changes from which it is calculated.
• Index point changes produce volatility measured in index points.
• Variance is expressed in squared units, while standard deviation uses the original units.
• Annualization changes the time scale of the estimate, not the type of unit.

Tags

# Normal vol - convention


# Normal vol - convention












apologies for the simplicity of the question, but I was wondering: what is the quoting convention for normal (bps) volatility?

Say I have the following time series of data:

Date Close Abs Change 20-Oct 1000.00 21-Oct 1003.53 3.53 22-Oct 1004.79 1.25 23-Oct 1009.88 5.09 24-Oct 1002.02 -7.86 25-Oct 1005.96 3.94 26-Oct 1004.96 -1.00 27-Oct 1008.30 3.33 28-Oct 1002.18 -6.12 29-Oct 1004.95 2.77 30-Oct 1000.95 -4.00 31-Oct 1008.19 7.24

It follows that the 10day realized (normal) vol (calculated as stdev of the abs changes) is 6.34, and the annualized vol is 100.75 (using an annualization factor of 252).

My question is: what units are these vol levels of 6.34 & 100.75 in? if the underlying was a stock index, would it be index pts (or in case of FX: pips/Big figures)?

Thanks in advance

## Answer by jaamor (score 1)

https://quant.stackexchange.com/a/15234

The unit for volatility is the same unit as the random variable. In the case of the index, yes, it is the index points.

The units of the variance is the unit of the random variable squared. Standard deviation is the square root of variance and has the same units as the random variable.

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