Volbox is an option market data visualization tool, centered on implied volatility (IV). We show:

1)     Volatility surfaces, a 3D theoretical representation of what IV would be if there were options available for every day and every strike price,

2)     Scatter plots, a 3D depiction of the IV of all listed options for a security,

3)     IV smiles which show how IV varies from strike price to strike price for a given expiration date, and

4)     the term-structure of IV depicting how IV differs from expiration date to expiration date, for a given strike price.

We provide implied volatility estimates for all contracts with maturities greater than 7 days forward.

Our proprietary smoothing algorithm then uses these data to generate a useful 3D visualization of IV across all strikes and maturities.

We do not estimate IV for so-called 0DTE options, or even options with 2-6 day expirations, as the results are not mathematically meaningful.

We omit options with 0 value or no bid.

Volatility is a word with multiple meanings in the securities and options markets.

Traders will refer to historical volatility, implied volatility and expected volatility.  

See below for the meaning of these different terms.

In 1973 Myron Scholes and Fisher Black developed the first equation designed to calculate the theoretical value of a call option. This equation required five inputs:

1)     The price of the underlying stock

2)     The strike (exercise) price of the call

3)     The number of days until the option’s expiration

4)     The risk-free interest rate

5)     The stock’s expected volatility over the term of the option.

The first four of these variables are easily observable: the price of the stock can be obtained simply be getting a quote, the exercise price of the option is fixed (it’s $50, $75, or $180), the number of days to expiration calculated using a calendar or calculator, and the risk-free rate is usually taken to mean the yield on US T-bills. The only sticking point is the stock’s volatility.

This is problematic because the volatility required is that of the stock over the term of the option, i.e., the future volatility of the stock. Very few traders have crystal balls capable of forecasting future volatility.

But wait! For most traders there is no need to calculate the theoretical price of an option. Options are traded on multiple exchanges and the current market price of an option is as easily observable as the current price of a stock.

So, we find ourselves in the following position: we can observe four of the five variables required to price an option and we can also observe the current price of the option. Using a bit of reverse engineering we can therefore calculate the expected volatility that the market is using to price this option. This backed-out volatility is the option’s implied volatility.

When you take as your starting point the current price of an option, and ask yourself “What volatility estimate do I have to use to obtain this price?”, you are asking “What is the implied volatility of this option?”

At first glance one would expect that the same volatility would be used to calculate all of the options prices (different exercise prices and different expirations) for a given stock or security.

Why would the stock’s volatility change for different options?

There is only one stock involved here.

But what we find is that the market assigns different expected volatilities across the various strikes and expirations.

What’s going on?

One example is out-of-the-money puts.

The surface normally, but not always, shows IV increasing as one moves deeper and deeper into-the-money.

What this reflects is that buyers of these options are willing to pay a higher price to meet the sellers’ demand.

Another common phenomenon is an increase in IV for options expiring shortly after an expected earnings’ announcement.

Options expiring before the announcement will have a lower IV, since the earnings news will not impact the stock price before the options expire.

Options expiring shortly after the expected earnings announcement will generally trade at a higher IV, since the full impact of the earnings announcement will impact the stock price and indirectly the options premiums.

The IV surface is a theoretical representation of options’ IV, assuming that options are trading for all possible strike prices and all possible expirations.

This surface is extrapolated from the IVs that can be calculated, i.e., the IVs of listed options.

To find out which options are listed and their IV, see the IV Scatter Plot.

You can! The Volbox IV surface integrates data from both calls and puts. For each option strike and expiration, there is a corresponding put and call pair. Their prices are governed by a fundamental principle in finance called put-call parity. This principle states that a portfolio comprising a long call option and a short put option is equivalent to a forward contract with the same strike price and expiration.

A key implication of put-call parity is that, in an ideal market, a put and a call with the same strike and expiration will share the same implied volatility (IV). By convention, IV surfaces typically display the IV for out-of-the-money (OTM) calls and puts. This approach is standard across the industry, as OTM options offer sharper insights due to higher liquidity and narrower bid-ask spreads, resulting in a more reliable fitted curve.ption

If an option has no bid (or a $0.00 bid) it will not be included in the volatility surface.

Also, options with extremely high implied volatility may also be excluded; these are most often short-term, out-of-the-money options with a relatively high asking price.

The graphed volatility surface stretches out one year from the date it is created.

If a security has options listed that expire in more than one year, these options will be taken into account in drawing the surface but will not be illustrated.

If a security has very few options that can be used to create a surface, the result can be quite peculiar.

In those instances, a better way to visualize a security’s IV may be the IV scatter plot, which lets you see all the actual data points.

A scatter plot graphs the data used to create a volatility surface along this same surface.

The dots on this graph represent existing data points: this is the strike price and expiration dates where options are listed.

The “ghost” surface is the theoretical surface that is created using the dots as a starting point.

Historical volatility is a measure of a security’s past volatility over a given time period.

For example, one can calculate 30-day, 90-day, 365-day volatility.

Because historical volatility looks only at the past, there is no room for argument: it was what it was.

Historical volatility is most often expressed as an annualized percentage.

Comparing historical to implied volatility gives an insight on market expectations: if implied is higher than historical, we can conclude that the market expects that the underlying security will be more volatile over the term of the option than it has been over the historical period, and vice versa.

For the mathematically inclined, historical volatility is the standard deviation of the daily rates of return of a security (using continuous compounding), annualized.

For the mathematically inclined, historical volatility is calculated from a security’s daily returns (it can also be calculated from weekly or monthly returns, but this is less common).

Look at the daily returns of stock A and B over a 10-day period:

Stock A: 1%, 1.5%, 0%, -1.2%, 0.4%, -2.1%, 0.8%, 1%, -0.2%, 1.9%

Stock B: 1.8%, 3.1%, 0%, -1.3, 0.2%, -2.9%, 0.8%, 1.6%, -0.5%, 2%

An eye-ball test will lead us to conclude that stock B is more volatile than stock A.

Calculating the standard deviation of these returns and annualizing, we find that stock A has a 18% volatility, and stock B a 27% volatility.

How did we get this result?

For the first list, the standard deviation is 1.17%.

Using mathematical shorthand, the annualized standard deviation is roughly 16 times the standard deviation of daily returns (16 is roughly the square root of 252, which is the number of trading days in a typical year).

Historical volatility looks at the past.

The volatility required to calculate option prices is the volatility of the security during the term of the option, i.e., future volatility.

For many securities, implied volatility is close to historical volatility.

The interpretation is that future volatility will closely mirror past volatility.

But in a significant number of cases, implied volatility is different from historical.

The interpretation here is that the market expects the future to be different from the past; it could be due to developments related to the underlying security (the nature of the business is changing) or expected announcements such as earnings.

The smile graphs IV for different strike prices for a given expiration.

Most often the smile will show the lowest volatilities at- or close-to-the-money, with higher IVs as on move away from the current stock price.

IVs for the smile are calculated from the out-of-the-money puts and the out-of-the-money calls.

IVs are shown for both options’ bid and ask.

The smile is usually the result of higher demand for out-of-the-money options which pushes up their prices and IV.

Smiles also tend to be more pronounced for the shorter term options; this reflects the fact that a given increase in the price of an option, say $0.10, will impact short-term options’ IV more than the same price increase for a longer-term option (remember that the longer-term option will be trading at a higher premium than the shorter-term option, and that $0.10 will be a greater percentage of the shorter-term option).

This graph shows IVs for one strike price across the different expirations.

The graph will have a dot if that data point is calculated from a listed option.

No dot means the data point is extrapolated from the Volatility Surface graph.

Bumps in the term-structure graph may indicate expected events; for example, options expiring after an expected earnings announcement may be trading at a higher volatility than options expiring prior to the announcement.