Historical Volatility

The historical volatility is defined as the standard deviation of the logarithmic price changes measured at regular intervals of time. Since settlement prices are usually considered the most reliable, the most common method of computing volatility involves using settlement‐to-settlement price changes. We defined each price change, x_i, as:

x_i = ln (P_i /P_{i – 1})

where Pi is the price of the underlying contract at the end of the i^th time interval.

P_i/P _i /P_{i – 1} is sometimes referred to as the price relative.

We first calculate the standard deviation of the logarithmic price changes:

standard deviation = √ 0.005778/9 
= √ . 000642
= .025338

We then calculate the annual volatility by multiplying the standard deviation by the square root of the time interval between price changes.

Since we looked at price changes every week, the time interval is 365/7:

annualized volatility = .025338 × √ 365/7
= .025338 × √ 52.14
= .025338 × 7.22
= .1829 (18.29%)

Reprinted from: Nathanberg, Sheldon. Option Volatility & Pricing,
Advanced Trading Strategies and Techniques, 2d ed.,
(Chicago: Probus Publishing, 1994), Appendix B.

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