# How to measure option put skew

By Simon Gleadall, CEO of Volcube.

Options on the same underlying and with the same expiration date often have different implied volatilities. This is known variously as the option smile or option skew. Traders often like to keep track of the amount of skew or smile in the particular markets in which they have an interest. This might be because they want to actively trade the curve or it could be information they take into account when initiating certain positions. For instance, if a trader is going to buy some downside protection for his portfolio, perhaps by buying puts, he might want to check out the current level of put skew *relative to historical values.* The result could affect his trading decision; if the put skew is currently cheap against historicals, perhaps this is a plus and he is more enthusiastic about the hedge. If the skew is rich, maybe the trader will look to other markets to hedge or postpone the hedge. The question is; how do traders measure the skew?

The primary goal of any measure of skew or smile or even kurtosis is consistency. The world changes and options’ lifespans change daily. So it is vital that traders are comparing like-with-like when it comes to any skew metric. Here we outline one typical approach that aims to be consistent across time and for changes to multiple variables.

### Measuring skew by option delta

This method is relatively simple. The trader picks an option which he believes gives a good reflection of skew. This is usually something like the 15% delta call or the -15% delta put. He then looks at the ratio of the implied volatility of the put or the call relative to the at-the-money option. So if the put has an implied volatility of 22% and the at-the-money implied volatility is 20%, the trader’s ratio is 1.1. This method has several advantages. Firstly, it is simple. Secondly, it has a nice degree of consistency for i) different absolute implied volatilities, ii) different spot prices and iii) different expiration dates. The metric can be used to compare the skew of say 1 month options and the 6 month options. Tracking the metric on a daily basis will begin to give a picture of the typical ranges the skew sits in for this product. Another related approach is to interpolate between different expiration to give an estimate of 30 day skew. So if the 20 day options have a skew metric of 1.1 and the 50 day options have a skew of 1.5, the weighted average (giving greater weight to the 20 day option, since it is closer to 30 days) would be around 1.2. Typical ratios that are tracked include put versus at-the-money, call versus at-the-money, put versus call and the same ratios across calendars.

Notice what this method does not do. It does not look at options in terms of strikes. It does not look at say ‘puts that have a strike $5 below the current at-the-money spot price’. This is because $5 is a fixed number but it means different things under different circumstances. If implied volatility is very high, $5 may not be a big price change in the underlying. Whereas if vol is low, $5 may be a huge gap. Also, $5 may not be a long way away when considering 12 month options. $5 to a 1 week option on the other hand could be an awful long way away. Percentage differences suffer from the same problem. Looking at say the ‘90% put’ is a method used by some (i.e. looking at the put with a strike 10% below the spot price), but it makes little sense. The relative magnitude of 10% will vary depending on the option’s duration. For a 1 month option, 10% can be huge; for a 2 year option, not such a big deal. Choosing options by their delta goes a long way to smoothing out these problems.

### Collecting the data

For traders without access to long term time series of option implied volatilities (and preferably option deltas), the old fashioned way of collecting a data point once a day or once a week in a spreadsheet might be the only solution. Nothing wrong with this of course, other than being labour-intensive and prone to gaps forming. It rather depends on why the trader wants the data. If it is purely as one of many indicators that are feeding into his trading decisions and the trader is focussed on only a handful of core markets, then this relaxed approach may be more than adequate compared to the expense of getting the data in a more automated fashion. For retail option traders, this is likely to be the case. Keeping an eye on the metric for their markets of interest can be worthwhile. In the past, some traders who favour ratio spreads for instance, follow the skew ratios keenly and are more or less likely to trade depending on where the skew ratio sits relative to its historical range.

For traders who take a more algorithmic approach and are looking to compare skew ratios across hundreds or thousands of option markets, obviously something more sophisticated will be required. Data feeds are probably more likely to be of use than settlement volatilities published by exchanges. The cost of such data is obviously a function of its freshness.

Gathering data from a quoted market, it is usually just a case of taking the mid-point as a value and inferring the implied volatility. Precision can depend on rounding and tick-sizes, so it usually doesn’t make sense to compute the ratio to too many decimal places.

Have a question for the author? Happy to help! Email [email protected].

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