Implied volatility (IV) is one of the most important concepts for options traders to understand for two reasons. First, it shows how volatile the market might be in the future. Second, implied volatility can help you calculate probability. This is a critical component of options trading which may be helpful when trying to determine the likelihood of a stock reaching a specific price by a certain time. Keep in mind that while these reasons may assist you when making trading decisions, implied volatility does not provide a forecast with respect to market direction.

Although implied volatility is viewed as an important piece of information, above all it is determined by using an option pricing model, which makes the data theoretical in nature. There is no guarantee these forecasts will be correct.

Understanding IV means you can enter an options trade knowing the market’s opinion each time. Too many traders incorrectly try to use IV to find bargains or over-inflated values, assuming IV is too high or too low. This interpretation overlooks an important point, however. Options trade at certain levels of implied volatility because of current market activity. In other words, market activity can help explain why an option is priced in a certain manner. Here we’ll show you how to use implied volatility to improve your trading. Specifically, we’ll define implied volatility, explain its relationship to probability, and demonstrate how it measures the odds of a successful trade.

## Historical vs. implied volatility

There are many different types of volatility, but options traders tend to focus on historical and implied volatilities. Historical volatility is the annualized standard deviation of past stock price movements. It measures the daily price changes in the stock over the past year.

In contrast, implied volatility (IV) is derived from an option’s price and shows what the market implies about the stock’s volatility in the future. Implied volatility is one of six inputs used in an options pricing model, but it’s the only one that is not directly observable in the market itself. IV can only be determined by knowing the other five variables and solving for it using a model. Implied volatility acts as a critical surrogate for option value – the higher the IV, the higher the option premium.

Since most option trading volume usually occurs in at-the-money (ATM) options, these are the contracts generally used to calculate IV. Once we know the price of the ATM options, we can use an options pricing model and a little algebra to solve for the implied volatility.

Some question this method, debating whether the chicken or the egg comes first. However, when you understand the way the most heavily traded options (the ATM strikes) tend to be priced, you can readily see the validity of this approach. If the options are liquid then the model does not usually determine the prices of the ATM options; instead, supply and demand become the driving forces. Many times market makers will stop using a model because its values cannot keep up with the changes in these forces fast enough. When asked, What is your market for this option? the market maker may reply What are you willing to pay? This means all the transactions in these heavily traded options are what is setting the option’s price. Starting from this real-world pricing action, then, we can derive the implied volatility using an options pricing model. Hence it is not the market markers setting the price or implied volatility; it’s actual order flow.

## Implied volatility as a trading tool

Implied volatility shows the market’s opinion of the stock’s potential moves, but it doesn’t forecast direction. If the implied volatility is high, the market thinks the stock has potential for large price swings in either direction, just as low IV implies the stock will not move as much by option expiration.

To option traders, implied volatility is more important than historical volatility because IV factors in all market expectations. If, for example, the company plans to announce earnings or expects a major court ruling, these events will affect the implied volatility of options that expire that same month. Implied volatility helps you gauge how much of an impact news may have on the underlying stock.

How can option traders use IV to make more informed trading decisions? IV offers an objective way to test forecasts and identify entry and exit points. With an option’s IV, you can calculate an expected range – the high and low of the stock by expiration. Implied volatility tells you whether the market agrees with your outlook, which helps you measure a trade’s risk and potential reward.

## Defining standard deviation

First, let’s define standard deviation and how it relates to IV. Then we’ll discuss how standard deviation can help set future expectations of a stock’s potential high and low prices – values that can help you make more informed trading decisions.

To understand how implied volatility can be useful, you first have to understand the biggest assumption made by people who build pricing models: the statistical distribution of prices. There are two main types which are used, normal distribution or lognormal distribution. The image below is of normal distribution, sometimes known as the bell-curve due to its appearance. Plainly stated, normal distribution gives equal chance of prices occurring either above or below the mean (which is shown here as $50). We are going to use normal distribution for simplicity’s sake. However, it is more common for market participants to use the lognormal variety.

Why, you ask? If we consider a stock at a price of $50, you could argue there is equal chance that the stock may increase or decrease in the future. However, the stock can only decrease to zero, whereas it can increase far above $100. Statistically speaking, then, there are more possible outcomes to the upside than the downside. Most standard investment vehicles work this way, which is why market participants tend to use lognormal distributions within their pricing models.

With that in mind, let’s get back to the bell-shaped curve (see Figure 1). A normal distribution of data means most numbers in a data set are close to the average, or mean value, and relatively few examples are at either extreme. In layman’s terms, stocks trade near the current price and rarely make an extreme move.

Let’s assume a stock trades at $50 with an implied volatility of 20% for the at-the-money (ATM) options. Statistically, IV is a proxy for standard deviation. If we assume a normal distribution of prices, we can calculate a one standard-deviation move for a stock by multiplying the stock’s price by the implied volatility of the at-the-money options:

One standard deviation move = $50 x 20% = $10

The first standard deviation is $10 above and below the stock’s current price, which means its normal expected range is between $40 and $60. Standard statistical formulas imply the stock will stay within this range 68% of the time (see Figure 1).

All volatilities are quoted on an annualized basis (unless stated otherwise), which means the market thinks the stock would most likely neither be below $40 or above $60 at the end of one year. Statistics also tell us the stock would remain between $30 and $70 – two standard deviations — 95% of the time. Furthermore it would trade between $20 and $80 – three standard deviations – 99% of the time. Another way to state this is there is a 5% chance that the stock price would be outside of the ranges for the second standard deviation and only a 1% chance of the same for the third standard deviation.

Keep in mind these numbers all pertain to a theoretical world. In actuality, there are occasions where a stock moves outside of the ranges set by the third standard deviation, and they may seem to happen more often than you would think. Does this mean standard deviation is not a valid tool to use while trading? Not necessarily. As with any model, if garbage goes in, garbage comes out. If you use incorrect implied volatility in your calculation, the results could appear as if a move beyond a third standard deviation is common, when statistics tell us it’s usually not. With that disclaimer aside, knowing the potential move of a stock which is implied by the option’s price is an important piece of information for all option traders.

## Standard deviation for specific time periods

Since we don’t always trade one-year options contracts, we must break down the first standard deviation range so that it can fit our desired time period (e.g. days left until expiration). The formula is:

(Note: it’s usually considered more accurate to use the number of trading days until expiration instead of calendar days. Therefore remember to use 252 – the total number of trading days in a year. As a short cut, many traders will use 16, since it is a whole number when solving for the square root of 256.)

Let’s assume we are dealing with a 30 calendar-day option contract. The first standard deviation would be calculated as:

A result of Ա 1.43 means the stock is expected to finish between $48.57 and $51.43 after 30 days (50 Ա 1.43). Figure 2 displays the results for 30, 60 and 90 calendar-day periods. The longer the time period, the increased potential for wider stock price swings. Remember implied volatility of 10% will be annualized, so you must always calculate the IV for the desired time period.

## Final thought

Hopefully by now you have a better feel for how useful implied volatility can be in your options trading. Not only does IV give you a sense for how volatile the market may be in the future, it can also help you determine the likelihood of a stock reaching a specific price by a certain time. That can be crucial information when you’re choosing specific options contracts to trade.

## Comment on this article

## Comments

cory on March 14, 2018 at 5:50pm

why do we take the square root of 30/365, and not just multiply by 30/365?

Balakumar R. on June 8, 2019 at 1:45am

This is an amazing explanation of IV and SD. Relation between both. hats off..thanks..

Ally on June 18, 2019 at 9:48am

We love comments like this. Thanks for reading.😊

Diego on August 20, 2019 at 12:28pm

Why do you divide by 365 if as mentioned there is only 252 trading days? If so you get a +/- 1.725 instead. Is this a more accurate model?

Ally on August 21, 2019 at 4:23pm

Hi Diego, it’s usually considered more accurate to use the number of trading days until expiration instead of calendar days. Thanks for your comment!

David D. on January 13, 2020 at 4:53pm

If in calculation we use 256 days instead of 365, for a 30 calendar days option contract, should we use sqrt(30/252) or sqrt(21/256) because there is 21 working days in 30 calendar days period. ?

kelly on May 9, 2020 at 7:19am

thank you for the great article.

Ally on May 9, 2020 at 8:19am

Hi Kelly, thanks for reading!

Dave on June 12, 2020 at 4:22pm

How would you punch 50 x .20 x Square root 30/365 in a calculator?

mike on July 25, 2020 at 9:25pm

Awesome explanation!!!...especially formula at bottom

Ally on July 25, 2020 at 9:55pm

We love comments like this! Thanks, Mike.

Emade D. on August 16, 2020 at 3:59pm

This article gives a thorough and simple explanation of implied volatility I've been looking for. It is much appreciated. Thank you.

Ally on August 16, 2020 at 4:21pm

Hi Emade, we love comments like this! Thanks for reading. 😊

Tom V. on December 6, 2020 at 12:09pm

Good until the end----I don't get when and where you use 16?

NManish on February 9, 2021 at 12:32am

What does it mean when implied volatility is above100%?

AK on February 15, 2021 at 10:01pm

Hi there! This was a really good explanation- thank you for writing it so well. The one question i have: When calculating your one standard deviation move, you get 1.43. You used 10% for implied volatility, should it be 20%? if not, where did you get the 10% from when the IV was 20%.

Albert P. on February 22, 2021 at 5:17pm

No definition of IV.

Brendan on March 7, 2021 at 5:54pm

I really like this article, it is very clear! However, I noticed that the article seems to conflate the mean price and the current price. In the example, it states "consider a stock at a price of $50...", but then later seems to use the $50 as the mean of the stock price when calculating a standard deviation move: "One standard deviation move = $50 x 20% = $10". It seems the calculation should use the mean stock price, not a single instance of the stock price, correct?

cosmin on August 23, 2021 at 5:02pm

The formula is applied only for at-the-money strike prices?

Arjun on August 29, 2021 at 12:10am

Excellent article, however Annual price could be considered population mean mean price, and daily price or monthly could be considered as a sample mean price of a stock

Daniel T. on September 27, 2021 at 1:38pm

In your last example on the page, you use an IV of 10%. Is that something you just assumed for the sake of demonstration, or is it derived from somewhere ? If the former, why did you assume that particular IV? If the latter, how did you derive it? Thanks!

Ally on September 27, 2021 at 1:39pm

Hi Daniel, our team would be happy to discuss this further with you if you’ll give us a call at 1-855-880-2559 or chat with us online at ally.com.

AshG on October 11, 2021 at 11:54am

Super Helpful! Thanks 😊

Ally on October 11, 2021 at 11:55am

Thanks for reading, Ash!