## What is Implied Volatility in Options?

In our article on the Black-Scholes formula, we explained that before the popularity of the Black-Scholes model, it was difficult for investors to evaluate whether an option was fairly priced. When the formula was developed, people became more confident with the idea that it is indeed possible to enter a perfectly hedged position. This is achieved by combining option contracts and their underlying securities when the contracts are priced accurately. Again, the Black-Scholes model only applies to European options that may only be exercised upon expiration day.

In that article, we also explained that one of the most important factors for pricing options is the volatility (implied volatility) of the underlying.

As a review, here is the modern Black-Scholes Formula for calls:

And here it is for puts:

- C stands for Call Premium.
- S is the stock price.
- K is the option strike price.
- T – t is the time remaining until expiration (or maturity).
- r is the risk free interest rate.
- e represents the irrational number that’s often called Euler’s number.
- N is cumulative standard normal distribution.

The first part in the equation represents the expected returns of purchasing the underlying asset. *SN(d _{1})* multiplies the stock price by the sensitivity in the call premium of the change in the underlying price. The second part,

*N(d*represents the current value of paying the exercise price of the option on expiration day. Getting the difference between the two parts gives investors the value of the option, or the call/put premium.

_{2})Ke^{-r(T-t)}Below are the formulas for getting the values of d1 and d2:

Where:

- S is the stock price.
- K is the option strike price.
- T – t is the time remaining until expiration (or maturity).
- r is the risk free interest rate.
- In is the natural logarithm.
- σ is the annual volatility of the stock (also referred to as standard deviation).

To refresh your memory, we explained that the option price is easily affected by volatility (σ) changes. However, since volatility is not easily determined, most of the time it is estimated from historical underlying security values or is derived from the Black Scholes formula. Stock price volatility is among the necessary factors that investors look into when calculating the premium of an option. And remember, volatility is simply the amount that the stock price fluctuates.

## What is the Difference Between Historical and Implied Volatility?

By definition, historical volatility is the annualized standard deviation of a stock’s price movements in the past. So, if a stock has large price swings on a day-to-day basis over the past year, it is historically a volatile stock with a high standard deviation.

On the other hand, implied volatility (IV) is not based on historical pricing. Instead, implied volatility is forward-looking. It is what the marketplace is “implying” a stock price’s volatility is right now, with current data. Implied volatility is an annualized figure.

Where then can implied volatility be derived? Simple: it is derived from the currently available cost of the option, where implied volatility will be calculated as a plug in the Black Scholes formula.

Since we know what the current option price (option premium) is, implied volatility is often what the formula actually calculates, not the premium price. If there were no options traded on a given stock, it will be difficult to calculate implied volatility.

Which brings us to the next question: how do we compute implied volatility?

## Calculating Implied Volatility

Would you buy an Apple stock without knowing the price? Naturally of course, you wouldn’t! But here’s the thing; many option traders buy and sell options without any serious regard for understanding implied volatility.

When you have the components for calculating the Call Premium (using the Black-Scholes formula), it actually becomes easy to compute a security’s implied volatility. Implied volatility is, arguably, the most important factor used to assess the affordability or the luxury of an option. You should not trade when you haven’t done your due diligence. It is extremely important for you to understand whether or not you are overpaying for an option. You need to get your money’s worth.

Let’s look at an example with the following data:

In this example, let’s say the last call option trade price was at $3.61. That value, versus the $3.13 call price which we calculated using the Black Scholes formula, means that we are way off. With the help of the Excel’s Goal Seek function (or you could try trial and error with different values using the Black Scholes formula) you can get the correct volatility which matches the last options trade price of $3.61.

This Goal Seek function requires three readily available variables. You just need to select your calculated call price as the “Set cell” (C9). Then input the $3.61 market value under the “To value” window. Then, set the “By changing cell” to your assigned cell (C6) for volatility on the Excel sheet. When you hit OK, the Goal Seek function figures out that the volatility for this particular stock is at 20%.

Here are the results. As you can see cell C6 changed to 20% as the correct volatility.

Today, investors and traders are luckier than ever because everything in the securities markets is transparent. With the World Wide Web, we see various market data – even a security’s highest implied volatility rates on a daily basis. When traders see that a security’s implied volatility is high, they become aggressive in selling that option. A lot of online market data also shows the percentage of the increase or decrease in volatility.

## When is High Implied Volatility Too High?

We now know that Implied Volatility plays a huge role in our analysis when it comes to buying or selling an option. Volatility of a security changes over time. When the Implied Volatility is low, buyers get the options for cheaper. When the Implied Volatility is high, buyers will pay more for the option. The opposite occurs for option sellers. They get more premium when the Implied Volatility is high and lower premium when Implied Volatility is low.

Now the question becomes when is implied volatility high enough to get our desired results? How do we know that the odds are in our favor? Well, we introduce you to the Implied Volatility Rank, or IV Rank.

Implied Volatility Rank (percentage) is used by many financial institutions to measure a stock’s Implied Volatility. To illustrate, when a stock has an IV Rank as high as 90%, this means that it has a lower implied volatility than the current one over the past year 90% of the time. This means that the current Implied Volatility is high, since it sits at least at the 90th percentile over the past year.

For example, if Microsoft has an IV Rank of 90% or higher today, then this means that we can expect it to go down over the next five days. When we assume that the IV Rank is mean-reverting (meaning we can always expect it to go down), then the IV Rank can help us in our trading decisions. We profit from an increase in IV for selling options.

We profit from a decrease in IV for buying options. IV Rank’s values run from 1 to 10, as we can see under column “Volatility” in the image below.

## Taking Advantage of Online Screeners

If you have an investment or financial advisor, who can walk you through the whole process because you simply don’t have the time – they can actually tell you the IV Rank of your chosen fund. Volatility charting are widely available online and the resources are just enormous.

There are actually three indicators (or charts) that you may opt to take advantage of when looking into your buying or selling opportunities.

One key thing to remember is that when the historical volatility is higher than the current implied volatility, the options might be undervalued. Meanwhile, the options become overvalued when there is higher implied volatility compared to historical. This is where **Volatility Forecast Scans** become a necessity. This online analyzer, available in various institutions, assists you in finding securities with volatilities that increase or decrease over the short- or long-term.

Another online analyzer that can help you gauge your opportunities is one that evaluates the **Implied Volatility Moves.** Securities with the largest moves in daily and monthly implied volatilities are observed with this type of scan. Analyzing the figures in this type of chart can help you assess, in advance, whether an upcoming event may have a large impact on the price of your fund’s options.

Lastly, take advantage of charts that show results of **Implied Volatility Scans.** These scans help you find securities that are either high or low risk, which is obviously necessary in your investment decision-making process.

To conclude, while our own knowledge and understanding, as well as manual calculations, help us make informed decisions when buying or selling European call options – there is absolutely nothing wrong with taking advantage of online trading tools. This can also be a perfect opportunity for you to get all your money’s worth with your investment advisor, if you have one.

## Why Implied Volatility is Important to Investors

The decision of option traders and investors in determining their best buying and selling strategies for a particular option depends on their analysis of that option’s implied volatility. An option’s premium price component changes where there are expectations of volatility changes over time. These volatility changes occur with supply and demand conditions affecting the underlying asset of an option as well as the expectations of the market with regard to its price direction. When an option’s underlying asset demand increases and the price goes up, implied volatility generally decreases. This will also result in a decrease in the premium price component. On the contrary, when an option’s underlying asset’s demand decreases and the stock price decreases, the implied volatility generally goes up, and options become more expensive.

To illustrate the idea behind Implied Volatility realistically, a security’s implied volatility increases during bearish markets when investors assume that the asset’s prices will reduce over time. On the other hand, a security’s implied volatility decreases in bullish markets when investors believe that the asset’s price will increase over time. This is generally the case since prices go down faster in a bear market than when they go up in a bullish market. Therefore, stock price fluctuations are greater in bearish markets when demand for equities is low.

For most option traders, implied volatility is more important than historical volatility because IV takes into account all market expectations. Various factors such as employee strikes, entrepreneurial errors, unfavorable litigations, political and legal policy changes that affect the business, bad management, changes in business location or succession, and other company or industry specific events are all factored in when implied volatility is seriously considered by traders and when buy and sell decisions are made. Business, market, and economic risk factors are always considered.

These are the things options traders must remember:

- Option prices are dependent on implied volatility.
- A higher IV means higher option prices.
- When big moves occur in implied volatility in just a short period of time, there will be big changes in option prices as well.
- Buyers must aim to buy options with a low implied volatility to pay less.
- Sellers must aim to sell options with a high implied volatility to gain more.

## Final Words

Understanding implied volatility, as well as the basic knowledge on how it is computed, can help traders and investors avoid committing poor investment decisions. Accounting for it is extremely necessary to ensure that you are not overpaying or underpaying. When one does not consider this seriously, he is up for a huge error. Both new and experienced traders should not fall into this trap.

There are various strategies that can be utilized so you can enjoy maximum results should you decide to buy or sell options. It is best to regularly conduct one-on-one meetings with your options and/or financial advisor (if you have one) to get a clear picture of how your investment portfolio is performing.

Remember that options, just like any investment vehicle, come with many risks. Many investors have different goals in mind when making investment decisions. Regardless of the decisions that you make, whether you buy or sell an option, steady your ground as to what your financial goals are. Being a successful investor is about looking into the amount of money that you have, how much you want to earn by a given point in time, and how much risk you can handle given all your financial constraints.