IMPLIED VOLATILITY EXPLANATION

by OptionPundit on January 13, 2007

How to use implied volatility to estimate how much a stock or index will move.

When the implied volatility of an option is 35%, what does that mean? Volatility is a measure of how much a stock can move over a specific amount of time, and is defined as the standard deviation of daily percentage changes of the stock price. Implied volatility is simply the volatility that makes the theoretical value of an option equal to the market price of an option.

Volatility is usually expressed in annual terms, and represents a one standard deviation move in the stock. Dip into any statistics book, and it’ll explain that one standard deviation, up and down, encompasses about two-thirds of all occurrences. So, two-thirds of the time, the stock with an implied volatility will theoretically be between up 35% and down 35% in one year. But how do you convert that to a more useful timeframe, when most of the options you trade expire in the next couple of months?

If you assume that a stock has an annualized volatility of 35%, how much might it move in 1 day, 1 week, or 1 month? Well, open that statistics book again and see that the standard deviation increases proportionately to the square root of time. So, if there are 252 days in a year, you want to multiply 35% by the square root of 1/252 to get the 1 standard deviation for 1 day. That comes out to about 2.2%. So, in one day, two-thirds of the time the stock will be between up and down 2.2%.

To get that number for any number of trading days from today, multiply 35% by the square root of the number of days/252. That is, for the range 5 days from now, multiply 35% by the square root of 5/252. For 20 days from now, multiply 35% by the square root of 20/252. So, in 5 days, theoretically two-thirds of the time the stock will between up and down 4.93%, and in 20 days, between up and down 9.86%.

You can use this data to gauge the risk of certain positions. Let’s look at short call verticals. The stock is $80, and April options have an average implied volatility of 40% and 15 days to expiration. Two-thirds of the time, the stock will theoretically be between up and down 9.76% in 15 days, or between 72.89 and 87.81. So, if you’re thinking about selling the 85/90 call vertical, there’s a pretty good chance that the short 85 calls will be in the money at expiration. If you don’t like that scenario, but still want to be short a call vertical, you may want to consider selling a 90/95 or a 95/100 call vertical instead. You won’t receive as much premium as if you sold the 85/90, but there’s less risk of the short options being in the money at expiration.

This calculation is no guarantee of what a stock will do, and is susceptible to changes in volatility. But it is one more tool you can use to become a more informed trader. The above extract is from RedOption (RO), one of my favorite sites for option’s education. This was an interesting article that I thought OptionPundit readers may find useful. Thanks to RO.

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{ 5 comments… read them below or add one }

1 Shivali January 14, 2007 at 8:41 am

OptionPundit,

Congratulations on the new look of site. I have been a reader of your blog at blogspot. But I think this site is much more user friendly and presents key information in a very simple and elegant way.

Thanks and keep up the good work

2 Gary February 21, 2007 at 10:13 am

OP,

In an attempt to apply the implied volatility to actual probability
I have the RUT Apr 740 / 750 & 880 / 890 Iron Condor. Please help
me with the formula that will identify the actual probability that
both short legs will expire worthless as of today. As of the
Feb 20th close the RUT was at $826.12 with 59 calendar days
remaining and an approximate implied volatility of 12.75%.

I understand ($826.12 * 12.75%) * (SR 59/365)= 1 std deviation,
but I cannot seem to figure out the precise formula to obtain
actual percent probabilities at a point in time.

Thank you,
Gary

3 OptionPundit February 21, 2007 at 10:55 am

Gary, a simple rule of thumb is to look at the delta of your short strike as that is a good proxy for probability vs going into complex calculations. As of today, the delta for 750 is 10% i.e. 90% chance that it will expire worthless and similarly delta for 880 is 9% i.e. 91% chane that it will expire worthless. I also use this benchmark to give me a good indication.

Hope this helps,

4 Tony Chai September 25, 2007 at 6:03 am

Hi OP :

Nice of you to point out that by looking at the delta you can have a rough gauge of whether your short position will end up in-the-money.

Keep up the good work and your consistent profit.

Tony

5 Ionspot April 17, 2012 at 10:52 pm

80 * .0976 = 7.808 (7.81)
80 + 7.81 = 87.81
80 – 7.81 = 72.19

In your penultimate paragraph above, you (or RedOption) have 72.89.
Very small correction for a 5+year article.

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