### Implied Volatility Surface: calculation and use

After quite a long break, we continue our series of educational newsletters. This one is dedicated to one of our most popular datasets: the Implied Volatility Surface (IV Surface).

#### General

In some cases, you do need to download the implied volatility data for further analysis, instead of just using our web site services. We understand this, and provide such an option in the Data Download Wizard (for historical data) and Daily Updates Wizard (for regular daily or weekly updates). There are three datasets available for download:

1. Individual contracts data - just closing bid/ask, IV, greeks, volume and open interest for each contract in the option chain.
2. IV Index - a kind of composite IV for a stock, see the detailed description here.
3. IV Surface - this is an intermediate between the datasets above; it contains implied volatility values, interpolated for a set of fixed maturities and moneyness points. The delta value is calculated for each point, to facilitate mapping between moneyness (strike) and delta - which is a more popular parameter among professional traders.

We will describe this IV surface dataset in detail in this newsletter; the last section outlines our plans of enhancing this dataset for many important purposes.

#### How the Surface is built

Volatility Surface for a certain stock and trade date represents implied volatility and delta, calculated for a set of virtual strikes and virtual expiries (terms). Implied volatility is calculated from individual options' data, by interpolation by strike and expiry. The standard Volatility Surface is calculated for the terms of 30, 60, 90, 120, 150, 180, 360 and 720 days and virtual strikes of 50 % through 150 % of the current underlying price, with the step of 10 %. So, you are getting 96 points of data for each stock and date, each of them representing a virtual option contract with a certain expiry and strike.

Only out-of-the-money options are used for building Volatility Surface, that is:

• Puts for virtual strikes 50, 60, 70, 80, 90, 100 % of the current underlying price
• Calls for virtual strikes 100, 110, 120, 130, 140, 150 % of the current underlying price

When you download the data from our site, you see two parameters in the dataset: call/put and out-of-the-moneyness (OTM). For example, Call OTM 30 represents strike of 130% of the spot, and Put OTM 30 - 70%. Of course, the dataset also contains strike and delta, so that you do not need to map moneyness, strike and delta manually.

Now, how the Surface is built, in plain words. We take the two nearest to each Surface term expiries, and two strikes, nearest to each virtual strike. Then, implied volatility is interpolated linearly between strikes and linearly by square root of days to expiry. The resulting value is implied vola in the Surface. After that, the delta value is calculated, using standard option pricing models, for the virtual option contract with the given virtual strike and expiry.

The quality of the Surface data is ensured by a set of automatic and manual checks of implied volatility data. However, the IV "in the wings" (for options far from the money) can be spiky, because of the lack of liquidity for these options.

#### How the Surface can be used

The most evident advantage of the Surface data is that it is standardized - as compared to the individual contracts data. This opens a bunch of opportunities to compare the IV levels, looking for an attractive trading opportunity:

• between different expiries and strikes (calendar, vertical or diagonal spreads)
• between different historical dates, to check the trend in IV behavior
• between different stocks (pair trading and other multi-stock strategies)

From the other point of view, IV Surface contains more information than the abovementioned IV Index dataset. The latter contains the data for near-ATM strikes only, so it does not tell much about, say, attractiveness of the vertical spread trade.

On our site, we use the IV Surface in the Spread Scanner service. It helps to find the delta-neutral spreads, or, more generally, trades with the desired level of delta.

#### Parameterized Surface

Our analytics are currently working hard on enhancing this useful instrument. We mean the parameterization of the surface - that is, delivering the parameters of the Surface, instead of "fistful of points". This assumes that the surface is described as a smooth function of the expiry and strike; it is expected to be more or less smooth along the historical date axis as well.

There are quite a few ways to parameterize the IV Surface, we are not going to discuss them all at the moment. One popular (especially, in FX world) method uses ATM Volatility, Skew (Risk Reversal) and Butterfly to describe the Surface for each expiry. This method can be rather easily applied to most of the indexes, but it is not always so with the stocks themselves. The lack of option liquidity and drastic jumps in stock price seems to require more sophistication. So, we are not naming the dates yet, but stay tuned - the parameterization of IV Surface is one of our important tasks for this year.