How do you calculate the standard deviation on a stock option with 30 days to expiration?

Answer 1

The implied volatility of an option is equal to one standard deviation, expressed as an annualized figure and as a percentage of the stock price.

To convert that figure to a standard deviation for a shorter period of time, divide it by the square root of the number of time periods per year. In this case, since there are approximately 12 30-day periods per year, and the square root of 12 is 3.464, you would divide by 3.464.

Example:

A stock is trading at $40 per share and an option on that stock which expires in 30 days has an implied volatility of 25%. Divide 25% by 3.464 to get one standard deviation is 7.22% of $40, or $2.89.

If you don't know what the implied volatility of the option is, you can use an options calculator, such as the one at

http://www.mdwoptions.com/OptionCalculator.html

to calculate it.