# Volatility Swaps: Directly Trading Realized Volatility

Volatility swaps are over-the-counter (OTC) instruments used to trade an asset’s realized volatility. Unlike options, which have directional (delta) risk, duration (theta) risk, and implied volatility (vega) risk, volatility swaps are a “pure play” on realized volatility.

In order for us to better understand volatility swaps, we’ll first need to understand realized volatility.

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## What is Realized Volatility?

Simply put, it’s the magnitude of daily price movements of an underlying over a period of time – typically 1 month. If implied volatility is the market’s best guess as to what will happen, realized volatility is a measure of what actually happened.

Let’s consider the 1-month implied volatility (IV30) on the S&P 500 (aka: the VIX index) on February 22 2023 at 4pm ET: 22.29. To determine whether the 1-month implied volatility (IV30) of 22.29 is higher (overstated), lower (understated), or exactly accurate, we’ll need to observe the S&P 500 daily price movements over the next month, do some math on those movements, then compare the resulting number against 22.29. In other words, it’ll take a month to know if implied volatility was “correct”.

There’s an index that tracks the S&P 500 daily price movements over a month: the 1-month realized volatility index, informally abbreviated as “RV21”. According to the realized volatility index methodology defined by S&P Global, there are always 21 trading days (read: observations) used when calculating the 1-month realized volatility index (RV21), hence the “21” in the abbreviation. As a general note, when calculating forward-looking or forecasted values such as VIX, calendar days are used. When calculating rearward-looking or actual/occurred values such as realized volatility, the number of observations are used.

Continuing the example, let’s calculate whether the February 22 2023 4pm ET IV30 value of 22.29 was overstated, understated, or exactly right.

Implied volatility on February 22 2023 overstated realized volatility by 475 basis points (all IV and RV values are percentages).

By repeating this process each trading day and plotting the results, we get the following graph:

*Note*: from January 2 1990 onward we used the VIX index and its corresponding underlying: SPX (the S&P 500 index). For dates prior to January 2 1990, we used the “old” VIX index, which has since been renamed to VXO, and its corresponding underlying: OEX (the S&P 100 index). Cboe explains the origins, histories, methodology differences and ticker changes on their website. The freely-available historical VIX (and VXO) data page on Cboe’s site provides a good starting point for this info.

If we want to express the idea that implied volatility often overstates realized volatility, what trade would accomplish this?

Perhaps we sell a put option on the S&P 500 (SPX)? If we sold an at-the-money (50-delta) strike, we would have lost money despite IV30 being greater than RV21; the index closed down by 1.35% over that month. Also, selling a put option only gives us exposure to half the potential volatility. We would need to also sell a call – collectively a strangle or straddle – to capture both sides. If we sell strikes that are farther out-of-the-money than where the index actually settled, we’re leaving money on the table for “overshooting” the thesis.

Maybe we short a VIX futures position? VIX futures converge with VIX (IV30) at expiration, not 1-month realized volatility (RV21), so that won’t work.

Ok, what if we sell a strangle on SPX and somehow perfectly, continuously, hedge all the price (delta) risk? FOMC is approaching and the US just experienced two bank failures, so VIX has spiked (despite modest moves in SPX) which has caused unrealized losses and increased margin requirements on the strangle position. What a headache. And as gamma ramps up prior to expiration, delta hedging becomes increasingly more expensive (and/or complicated) to hedge. This won’t work either.

If only there was a way to trade just the IV30-RV21 spread. This is where volatility swaps come into play.

## Trading Volatility Swaps

Volatility swaps can be used in scenarios like:

- Hedging existing volatility positions
- Speculating on an asset’s volatility at a future date
- Trading the spread between implied and realized volatility

Consider Hank, a fictitious proprietary volatility trader. Hank notices that the VIX is currently 31.2 and believes that the 30-day realized volatility will be in the low 20s. Hank calls up an investment bank and states he wishes to sell a 30-day volatility swap on the S&P 500. The contract expires 30 calendar days from today and Hank requests a notional value of $100,000 (there is no transfer of funds, this is simply the basis of the OTC contract). The VIX is 31.2, so this is set as the contract strike price.

After 30 calendar days, despite VIX being at 28.3, realized volatility was calculated to be 23.2. This represents an 800 basis point difference, or $8,000 ($100,000 * 8%). The buyer of the volatility swap pays Hank $8,000.

If realized volatility was instead 33, Hank pays the buyer of the volatility swap $1,800 ($100,000 * 1.8%).

## Historical Performance of Volatility Swaps

### Average Spreads

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### Minimum Spreads

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### Maximum Spreads

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### Positive and Negative Spreads

## Summary

Consolidating the average, minimum and maximum datapoints into a single chart yields the following:

At first pass, this seems like a reasonable trade.

If we were to expand on this idea, we’d perform a backtest that explores the performance of opening a short 1-month volatility swap on SPX each trading day and see if there are any discernible trends.

We would also want to get an understanding of typical performance bond (margin) requirements for such positions and the costs a counterparty would charge to take the trade (and hedge their exposure).

Most importantly, we would need a way to trade these. Volatility swaps are institutional instruments that aren’t available to retail traders. Reproducing volatility swap payoffs would require a material amount of savvy, cost and time.

Pratap Prabhu

April 2, 2023 @ 2:36 pm

Great post. In theory, won’t the cost of hedging (trading cost) eat up any delta between RV and IV? I doubt these OTC contracts are cheap for retail

spintwig.com

April 2, 2023 @ 10:16 pm

Thanks!

Not necessarily. Delta hedging with long/short underlying is free at most retail brokers, sans a few pennies when selling shares. Counterparties that would be willing to take the other side are likely to incur nominal incremental costs to hedge their position. Some of the largest players are likely to generate revenue on their trading in the form of rebates.

The difficult part of doing it yourself is the automation (or not) of the delta-hedging trades, the adjusting of the option strip, and staying below the threshold to not be classified as “professional”. That designation comes with headwinds in the form of potentially less favorable fills and higher fees for market data.