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Why Do We Care About Volatility? part 3: Calculating implied volatility
Brian Overby
February 7, 2006

Welcome back to my series on “Why Do We Care About Volatility?” Last week I walked through some math to explain standard deviation, a crucial statistics term that helps you estimate the likelihood and size of a security’s price swings in a one-year period. Today you’ll find out how to apply that information to any time period.

All volatility figures are quoted on an annualized basis unless stated otherwise. Since we did not state otherwise in last weeks example, the marketplace thinks that “most likely” the underlying stock will not be below 80 or above 120 at the end of one year. “Most likely” is defined as in 68% of all occurrences.

Our next move is to break down the one standard deviation move so that it fits any time period – that way you can apply it to any expirations you’re interested in trading. The formula in the simplest form is the following:
OSDM = Price x Implied Volatility (ann.) x (sqrt) Calendar Days to Exp.

(sqrt) 365

(A more accurate formula is to use trading days to expiration instead of calendar days, and then divide the entire equation by (sqrt) 252, which is the total number of trading days in a year.)

Now let’s assume we are dealing with a 30 trading day option contract. The one standard deviation move then becomes:

OSDM = 100 x .20 x (sqrt) 30

(sqrt)365

OSDM = + 5.73

This means over a 30 calendar day period the underlying is expected to finish between 94.27 and 105.73. If we perform the calculations for a 60 and 90 calendar day period and then graphed the results the graph would look like the following:



This shows us that the longer the time period, the larger the potential for wider swings in the underlying stock. Keep in mind that even if you are looking at a 30, 60, or 90 day options the implied volatility will always be quoted as an annualized number.