So You’ve Heard About Gamma Exposure (GEX). But What About Vanna and Charm Exposures?
We’ve released a brand new chart service showcasing these advanced but potentially powerful greek-based dealer exposure metrics. We think they can be potentially powerful indicators.
Update May 2024: We’re spinning off most of the content in this article to a new product, Vanna Charm, which is heavily under construction, at Vanna Charm (https://vannacharm.com). Stay tuned for updates as we develop Vanna Charm.
The Wheel Screener is a trader-friendly option screener that analyzes, classifies, and categorizes all options available on the market on a given day. The team is always more than happy to share their technical insights, market opinions, and methodologies here on Medium. This article focuses on new metrics we are developing concerning Gamma, Vanna, and Charm exposures. We hope you enjoy the article!
Author’s Note: While we do reference spot price gamma as well as spot gamma, we would like to highlight that we are in no way related to or sponsored by SpotGamma (although somewhat inspired by them!). Also, we are NOT using the term “SpotGamma”, their proprietary indicator, but rather the widely known (among the trading community) mathematical gamma exposure, based on both gamma and the spot price as tabulated in the post below. Additionally, as always, none of this is investment advice. Always consult with a professional before making any investment decisions.
Gamma — A Tale of 2021 & 2022
In the past few years, retail traders, especially retail options traders have become savvier and savvier about the various options greeks. Ever since the GME meme stock craze of early 2021, 2021, and 2022 were all about traders and the market at large learning about and using gamma indicators in a widespread fashion, and that it could be used to potentially predict the size and speed of moves. It could even be used to potentially target or attempt to harm dealers, in the concept of “weaponized gamma”, coined by the great platform SpotGamma (again, we have no affiliations and are not sponsored by them, just fans!).
Vanna and Charm — 2023 and the Future
We believe that included in 2023 is the story of Vanna and Charm, the two other second-order options greeks. Put succinctly, while Gamma describes the change in the price of an option with respect to price twice, Vanna describes the change in the price of an option with respect to the change in the underlying price and change in underlying volatility, and Charm describes the change in the price of an option with respect to the change in the underlying price and change in time.
In shorter form:
Gamma = dV/dS² = change in option price with change in respect to underlying price twice
Vanna = dV/dSdσ = change in option price with respect to both underlying price and underlying volatility
Charm = dV/dSdτ = change in option price with respect to both underlying price and time
Gamma, Vanna, and Charm, the Three Greeks as Exposures (GEX, VEX, and CEX)
The story gets even more interesting if we take the perspective of dealers. If we take a look at all options activity for a given symbol, we can develop a concept of total Gamma, Vanna, and Charm exposure that dealers have on their books. Gamma exposure is the most well-known. It is defined as the change in dollar exposure per 1 percent of move in the underlying. It is often expressed as the following:
GammaExposure = callOpenInterest*CallGamma*100*spotPrice*spotPrice*0.01 - putOpenInterest*PutGamma*100*spotPrice*spotPrice*0.01
But since the contract size of 100 shares of the underlying and the percent move of 0.01 result in 1, those terms can be dropped out and we can express spot price Gamma exposure simply as:
GammaExposure = openInterest*gamma*spotPrice*spotPrice
However, this parameterization is important to remember as we’ll see below for Vanna and Charm.
At Option Screener, we’ve followed the same thinking to Vanna and Charm, as a way to express Vanna exposure and Charm exposure. Just as Gamma exposure is defined in dollars per 1% move in the underlying, we’ve defined Vanna exposure in dollars per 1% change in underlying volatility, and Charm exposure in dollars per 1 day change in time. It’s slightly more complicated than gamma exposure, however, mainly due to the signs of Gamma, Vanna, and Charm, depending on various factors that determine Vanna and Charm’s arithmetic sign. Let’s review them:
Gamma:
- Positive for call options
- Negative for put options
Vanna:
- Positive for call options
- Negative for put options
Charm:
- Positive for in-the-money calls and out-of-the-money puts
- Negative for in-the-money puts and out-of-the-money calls
Following a similar pattern as the Gamma exposure calculations, we take the Vanna and Charm exposures respectively to be:
VannaExposure = callOptionOpenInterest*CallVanna*spotPrice*underlyingVolatility + putOptionOpenInterest*PutVanna*spotPrice*underlyingVolatility
CharmExposure = callOptionOpenInterest*CallCharm*spotPrice*365 + putCallOptionOpenInterest*PutCharm*spotPrice*365
Note that in the Charm exposure calculation, we multiply by an additional 365 because the way we calculate our greeks, Charm is already expressed per day, i.e. divided by 365 — this is typically how Charm (and Theta for that matter though not relevant here) are often reported.
Each of these calculations can be plotted at every strike, and furthermore, at every expiration. We can get quite some pretty graphs, like the ones you can find for Gamma, Vanna, and Charm here.
Shares to Cover and Implied Move
It’s finally time for the ‘future’ predicting and sorcerer-like 🧙♂️ capabilities these structural flows can bring about that all those cool guys on the financial podcasts are always talking about!
When we take those pretty looking exposure-per-strike Gamma, Vanna, and Charm plots, and add them all up (for a fixed expiration but at all strikes), we get the net theoretical exposure that dealers could have on their books. Such a chart looks like this. From there, we can calculate the total shares of the underlying needed to cover said position, even calculating what this covering action might mean as to how the underlying moves! (bar chart below the 7-day trends). This is a bit of comparing apples to oranges, as Gamma exposure concerns changes in the underlying, Vanna changes in the underlying’s volatility, and Charm change in time, but we think it is a decent first-order view of what option-based liquidity exposure dealers have. Indeed, taking today as an example (February 6th, 2023 when this was published) we had massive (though near equal) exposures on both sides of SPY:
And sure enough, all day SPY knocked around between these $408 and $411 levels:
It’s almost like there were some mysterious forces holding it between those values… hmmm…
Now, this could be totally anecdotal, but it’s exciting to us if this works sometimes as an indicator of price action in the underlying (or at least tendency of price action on the underlying. There’s more we could do here too, like expressing the net exposure as a total percent of the volume of underlying that is traded per day.
Also note there is an ongoing issue we are investigating, namely that the Charm exposures start to explode in size as we approach 0 time to expiry. We think it has something to do with the way we have scaled our Charm exposure equation and need to take another look at the parameterization of that equation. Any pointers here on what we missed are greatly appreciated!
Drawbacks
If you think it sounds too good to be true and we’ve solved the entire stock market — you’re right! As with every analytical tool out there, there are drawbacks to these exposure curves. The most major one is that they rely on the open interest of options contracts. Unfortunately, for most retail traders (and perhaps even larger firms?), that means the ability to calculate these exposures is limited to once per day after the open interest numbers are posted by entities like the CBOE. We’re not sure when this occurs exactly each day, and perhaps it’s not consistent, but it’s certainly at minimum a few minutes after the close as all the massive traffic numbers are tabulated.
Notional Intraday Change in Gamma, Vanna, and Charm Exposure
However, here at Option Screener and The Wheel Screener, we’ve started to develop a way to combat this missing data, in an attempt to calculate near real-time changes in Gamma, Vanna, and Charm, developing the concept of a notional intraday change in Gamma, Vanna, and Charm. Here’s how we are trying to calculate it:
- Take an expiration date, and all options available at all strikes for that expiry.
- For each strike, and option type (put or call), look at the bid-ask and volume numbers of both the put and call contracts. Calculate the bid/ask ratio.
- Assume that the volume is completely satisfied by the current bid/ask ratio. For example, if in a minute interval, we see 100 contracts traded and the bid/ask ratio is .6, We assume of those 100 contracts 60 were bought and 40 were sold.
- Finally, calculate this notional change in Gamma, Vanna, and Charm exposure. Here are the equations we use (very similar to the exposure equations above):
dGammaExposure = (totalContractsBought — totalContractsSold)*Gamma*spotPrice*spotPrice
dVannaExposure = (totalCallContractsBought — totalCallContractsSold)*CallVanna*spotPrice*underlyingVolatility + (totalPutContractsBought — totalPutContractsSold)*PutVanna*spotPrice*underlyingVolatility
dCharmExposure = (totalCallContractsBought — totalCallContractsSold)*CallCharm*spotPrice*(1/365) + (totalPutContractsBought — totalPutContractsSold)*PutCharm*spotPrice*(1/365)
Of course, this method is limited by the fact that the bid-ask ratio doesn’t tell you the actual buys and sells of each contract, nor does the volume tell you which direction options are going (sold or bought).
Our initial studies have shown that indeed this data is too noisy to be useful, but that’s up for further investigation, and I may have a specialist in signal processing and smoothing functions come in to give his two cents on a better way (if any) to glean any sort of trends from this noisy data.
The Charts
Probably what you’ve been waiting for, we’ve saved the best for last. Here are links to all the different ways we plot our Gamma, Vanna, and Charm exposure charts!
Total exposure trends over the next 7 days
Gamma exposure over the next 7 days
Vanna exposure over the next 7 days
Charm exposure over the next 7 days
Net exposure over the next 7 days
Normalized exposures per the next 7 days (1 chart per day)
The 0DTE Newsletter
If these structural flow analyses and overviews are interesting to you, and / or you are a 0–7DTE trader on indexes like SPY, SPX, and QQQ, we are also starting a daily 0–7DTE newsletter that will give a 2-minute rundown of these values in addition to information like put/call walls, put/call ratios, and so on. DM us on Twitter to be added to the list!
Thanks!
What do you think of our exposure calculations and our ideas about this new notional intraday change in Gamma, Vanna, and Charm? We are studying these new metrics and seeing if they are of any use in our 0DTE trades.
We’re on a mission to make options data accessible and a 100% customizable dashboard for any trader, from beginner to advanced.
Interested in learning more? Check us out at The Wheel Screener and Vanna Charm.
Until next time,
-The Wheel Screener Team
References and Further Reading
Many helpful resources were used to create the formulas, codes, and this post:
