Normal vol - convention

Question

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 1

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.